Firstly, the last thing I would ever want is for you to feel bad about falling into this particular habit. I myself was guilty of it for a very long time until I finally figured out that it was not only not helping me, but it was actually hindering my progress in mixing. Hi folks, I'm Mike and I hope you're well. Today we're going to be discussing why you should stop using presets with your plugins. Not only are they not that helpful with mixing, but they also have the potential to slow down your learning. Now with every rule there are exceptions, so we'll be discussing those a little bit later on. But first of all, let's talk about a type of plugin where I think presets are really unhelpful, and that's EQ. So in this project, I've got two vocal recordings. You can see them here in green and in blue. Now they're both exactly the same vocal performance by the same singer recorded at exactly the same time, but in two slightly different ways, which I'll explain later. But first of all, I want to sculpt the sound of these recordings, and I'm going to sculpt the sound using an EQ plugin. So I'm going to go to the first recording here, the green one, I'll go to my insert effects, I'll click on plus, go to insert audio effects, and I'm going to choose my favorite EQ that's pro q3 by a fab filter. Now this is a female vocal and it is or I'm wanting it to be kind of poppy. So I'm going to go across to my presets here and select the female pop vocal. Okay, there it is. It's done. It's trick of course should sound great. Let's wait and see. Okay, so I want to apply the same effect of course, through the other vocal recording. So I'll just close that. And here in Katewalk, I can just hold control on the keyboard, drag that first one across to the second one there. And not only has it got the same plugin inserted there, but it's also got exactly the same settings applied. Okay, let's have a listen to each of them in turn and see if we can hear a difference. So I'll solo the first one. Here we go. Okay, sounds not too bad. Let's go to the second one. Not only is it different, but it's kind of really harsh, isn't it? There's a really big difference that I really wouldn't want that as a result to be honest with you. So if I've applied exactly the same preset, why am I getting two completely different results and sort of fairly unpredictable results if I'm honest with you? Well, the reason is the nature of EQ doesn't really lend itself to using presets in this way. Let me explain. I'll go into Pro Q3 here. Let's have a look at one of the settings in here. I'm just going to look at this second setting here. So what this setting is saying is at 60 Hertz, let's reduce the signal by three decibels. In other words, for the part of the sound, which is at 60 Hertz, let's just turn it down by three decibels. Importantly, it's not saying at 60 Hertz, let's set the value to minus three decibels. It isn't an absolute setting like that. It's a relative setting, whatever the signal is. So if it's currently at, say, 10 decibels, it's going to reduce it by three and make it seven decibels. That's a simple explanation. So you can see that the result entirely depends on the input on the sound we're getting. You're going to get a different result depending on the actual recording. Now, these recordings were recorded exactly the same time by the same singer, same performance, as I said. So what is actually different about them? Well, firstly, they're recorded on two separate microphones. I actually got the two microphones and I put the capsules really, really close together and had the singer sing into both of them at the same time. So different microphones can have a different sound to them. Now, we happen to be using the same singer, of course, at this time, but obviously I hope you would understand that different singers also sound different. The distance of the singer from the microphone, if we get further away, yeah, things sound more teeny. If we get close, things sound deeper. That's a proximity effect. So that really affects the low end a lot. So all of these things can change the input signal. In addition, with this second one here, I recorded this with the Rode NT1A microphone. I also had it going through a preamp and a compressor on the way in, okay. So that was changing the sound before I even got to my interface with the recording. Different sound, different results with the same preset. And that is why presets with EQ are very, very rarely useful to you. Now, EQ, of course, is not only used to create a tone. Let me step back a bit.  Yeah, just like a tone control on your guitar or on your stereo system where it would have bass, mid, treble, something like that. Now, in some sense, yes, it is like that. It changes things in a similar way to those controls that you see on a guitar or on an amplifier or on a stereo system. But in mixing, EQ also has another purpose. You see, some instruments or sounds share the same frequencies, a lot of common frequencies. You can get this effect of one thing masking out another, let's say you've got a piano part, which shares a lot of the same frequencies as the vocal part. That will have the effect of not really both of them being present, but one will tend to cancel the other one out. So EQ is often used in mixing to carve out spaces so that one thing can shine, okay. That's a simplistic explanation, but it means that the EQ for this purpose is also dependent upon what else is going on in the song. And of course, the preset cannot know what else is going on in the song. So even in this case, where we're using a preset for something as common as a vocal, the final sound of the vocal in the mix will be very, very dependent upon the other things which are present in the mix. So as I say, EQ is commonly used in mixing. Another plugin which is very commonly used is compression. So in this project, I have a kick drum and I want it to sound really nice and tight. So I've got a compressor, which I've got inserted here on the kick drum channel. And I am going to select as a preset kick tight, okay. It's put in the settings there. Now what we're going to do is have a listen to this with the plugin applied and without the plugin applied.  I want you to use your ears here, okay.  Let's go.  Now if you could hear the difference between those two, I'm afraid that your mind has been playing tricks on you because there was no difference in the actual sound because the settings from this compressor are not set correctly to actually make a change. Let's bring it up again. The main setting for a compressor or one of the main settings for a compressor is the threshold, okay. This is the stage at which we start compressing the signal. Now at the moment you can see it's set to minus 13 dB or so. Let's just see where the signal is reaching with this kick drum. You can see it's only getting up to about minus 20 dB. So it's not even going over the threshold and even starting to compress. This really crude example is showing you that a compressor is highly dependent upon the input that it receives. It can't even start compressing if it doesn't have enough input for example. Beyond that, things like the ratio and the attack and the release are also affected by this signal that it's receiving. Now the main reason why you're probably using a preset with your compressor is because you don't really understand how to use compression and that's fine. We were all at that point once. I'm going to show you a video towards the end of this video. I'm going to put a link for another video that I made about compression, the basics of it and many people have told me that once they watch that video they finally understood what the controls on a compressor were actually doing. I'm going to leave that to the end of the video because I don't want you to go there quite yet because I've got some important information for you here. Now one of the things I would suggest before you go and learn how to use a compressor is to start to think about the differences in different sounds from different instruments. Let's close this down here and I'm going to go to another part of this project. I'll just get rid of the console. You can see that I've got two wave files here. I'll just zoom in so that we can see them a bit more clearly and we have a snare drum here and a bass guitar. Now what I want you to do is just look at these two waveforms and think about how different they are. The snare drum for example has a really quick attack there yeah and it quickly decays. That sort of spike that you can see at the beginning there is generally referred to as a transient okay. That's the initial impact of the sound often with drums, not with all drums but a lot of drum sounds. It's very quick and then it decays very very quickly. The second waveform we're seeing here is a bass guitar. Now I've also got a reasonably quick attack on this or transient but you can see that it decays much much more slowly over time until the bass player takes their finger off of the note. So there's some important things to remember here. If you wanted to change the initial impact of something with a compressor then you will be looking at that attack or that transient and you would use the attack primarily in combination with the threshold and the ratio. The ratio is going to control how much you compress the signal, how much you turn it down by. So compression is about understanding controls, understanding the nature of the sound that you're processing and making a plan. Probably the most important thing is making a plan. What do I want to do with this? How do I want to change, for example, this bass guitar? Do I want to have it have a quick impact and then die away or do I want it to be sustained? Do I want to keep that note alive for a long time? Those are the things we want to be asking ourselves with compression. So I'm afraid to tell you there's no real shortcuts with things like compression. However, you can understand it's not beyond you. You just need to have it explained to you in the right way. So EQ and compression make up a massive amount of what you do when you're creating a great mix. However, they depend highly upon the input they receive to get a great result. Manufacturers can't know what that input is when they're creating a preset and therefore the results going to be unpredictable and the whole time that you're using them you're not learning how to create those sounds yourself. So I would strongly recommend that you put a little bit of time into learning about EQ and compression rather than using presets. Now there are times where presets can be useful and it's usually with plugins that don't depend so heavily upon their input. Let's discuss some of those scenarios now. So one of the reasons I think you may make good use of presets is for something that I'll call stylized effects. These are sounds that have a particular style to them. So for example, let's think about vocals say in the 1950s, they had that huge echo on them. Now they weren't intended to sound like that person was in this massive space or heavy. It was just a sort of a style to that I guess people liked. Now if you just wanted to recreate that with some 1950s echo or reverb preset, I think that would be absolutely fine. Especially because it's not really that dependent upon the input that it's receiving. Yeah, it's going to do the same thing to any particular voice that it's receiving to get that style. Another occasion where this is really strongly true would be presets for guitar amp sims. For example, you think to yourself, hey, I just want to get that basic sound that Brian May gets. Yeah, there's probably a preset for that. And it's going to get you there really quickly choosing an appropriate sort of amp and cabinet and what have you. However, I would still caution with this that it's probably not going to be exactly the same because it's still depending upon the basic tone of your guitar, the settings that you have on your guitar, maybe even your fingers and your style of picking, etc. But in my experience, it can get you a long way there as a kind of a starting point. So one great use of the preset functionality for your plugins is using custom presets. These are presets you create yourself where you know you want a similar outcome each time and the inputs going to be similar each time. For example, with my own voice on my videos, because I'm always recording my voice in the same room with the microphone at a similar distance each time, I do have some presets for different situations where I record my voice. That can happen with a vocal on an album, for example, as well. If you've got roughly the same kind of a setup from song to song on an album, and you want to make sure you maintain a consistency in sound, then you may go for some presets so that you can quickly set up the sound of your vocal for each track. So yeah, it's kind of useful to use that functionality of your plugins. So I can certainly see a scenario where presets could be used as a learning tool also. Let's go back to our example of using compression. I still feel that it's best not to use presets, but if you're really not sure about what kind of attack and release settings to use for specific instruments, then it may help you to learn up a preset relating to that instrument and try and sort of reverse engineer what you're seeing. As I say, you're still going to have to adjust things like the threshold, but you could use that for a little bit of learning. So I know you just want to move on and create that fantastic mix, and there's a lot to learn about mixing. So presets seems like a viable option, but you're only doing yourself a disservice, especially in terms of actually learning about this craft yourself. Now, some things are particularly difficult to get your head around, and it seems like for most people, compression is one of those. That's why I made this video about compression, explaining what the common controls do so there's no longer a mystery to you. I reckon you should watch that right now.


Now, you're saying achieving your full potential is not happiness. How did this happen? See, tell me, what is the greatest pleasure in your life? Moments of accomplishment, success, yes or no? Is it so or no? It could be in personal life, it could be in professional life, it could be in social life. But when you get to do something well, that is when you're happy, isn't it? It could be a small thing, it could be a big thing. It may be a great activity or it may be you just hit the ball straight. You know, the amount of joy a lot of people are not coming home from the golf course because they hit it straight one day. So the question is not about this or that. In human life, the purpose of activity is success, any activity. If you perform some activity, you want to do it successfully, isn't it? Don't think your children don't have it, they also have it. Only thing is, because you're nagging them continuously, they want to do something just reverse. Because reverse, they understand as revolution. Don't push them into that revolution. If they have to evolve, you have to show evolution.  They're observing how you live. I want you today to put yourself through serious audit and make yourself tomorrow morning the way your children would love you. Your child doesn't need a boss. Your child needs a friend. Tell me when you were growing up, if you had some issues and problems within yourself, did you first go to your parents or to your friends? Friends, unfortunate, isn't it? Unqualified advice will happen among the friends. If you were their friend, real friend, not the boss that everybody's trying to be, if you were a genuine friend to your child, he or she would come to you first. That would be great, isn't it? Please make that happen.


I'm Reverend Bill Lewis, the Associate Pastor and Director of Outreach at Flower Man United Methodist Church where I serve with our senior pastor, Holly Gotelli. And it's my pleasure to present to you Caroline Farish, our 2017 Harry Dimmond Evangelism Award winner for youth. Caroline is a junior at the Shelton School in Dallas where she's president of Chargers for Change on the Varsity Tennis Team and in National Honor Society. Congratulations Caroline on winning the Harry Dimmond Evangelism Award. Thank you. First, let's talk about Caroline about your work with the Boral Boone Methodist Church and School in Belize. Five years ago we began an annual week-long mission trip to serve the people of Boral Boone Methodist School. Our work there is divided between doing VBS and various maintenance and construction projects for the school. I love our work in Belize because year after year we make a real difference in the lives of the people there. But what I love most are the relationships we've shared. Here's why Reverend James Williams, the Superintendent Minister of the Methodist Circuit in Belize wrote, Caroline has a special connection to children and people in general and her sweet disposition and innate ability to interact with people make her a natural when it comes to sharing about Jesus. Caroline, tell us about why writing the devotionals this year was so important.  God wants to introduce us to people whom we may not know so that we can introduce them to the God who knows and loves them. So together we can live out the salvation story. I wanted our team to live into this big idea. So I wrote a series of devotionals, one for each day of our journey, and it invited us to think deeply and spiritually about the work, about the relationships of the people we serve and with one another, and about each of our relationships with God. Now there's work right here in the North Texas Conference that you're doing as well. Tell us about that new thing you're doing at school. Right, so in January with all the stuff going on in our country after the election, I began seeing signs that kids in my school aren't being as kind and thoughtful as they could be. Now I believe that sheltering kids deep down are kind, thoughtful people, but we needed something to bring that kindness to the surface. That's where Project Kindness came in. Phase one of Project Kindness was an each-home room class. We asked every student and teacher to write their name in the center of a piece of paper, then pass it around so that everyone could write messages sharing what they valued about the person in the center of the page. At the end, each person got something she or he could hold on to and was filled with words of encouragement and appreciation, not only for what they did, but for who they are. Phase two, we created over a thousand sticky notes, messages of encouragement, which were placed on the main bulletin board so that when any student saw another student having a bad day, they could grab one of the sticky notes and put it on the student's notebook, locker, backpack, whatever, as a sign of support and caring, a not so random act of kindness. How'd that go, Caroline? We just handed 300 kids in our high school and all the thousands sticky notes were gone in a week. My name is Zach Ladd. I'm Dean of Students at the Sheltered School for the Upper School of 9th through 12th graders. Earlier this semester, maybe even late last semester, Caroline came to me with the idea for Project Kindness. She made the project her own and had a great time with it, involved others, and I think it helps others see Caroline doing this and realize they can do something too. Project Kindness will begin again when school starts, but there is another project that I'm very excited about too. It's called Peace, which stands for People Encouraging Awareness in Creating Equality. Peace will be a student-led series of honest conversations about race, religion, and social-economic status that we believe will allow our students to understand and respect one another better. She wants to make sure she understands her faith. She seeks to understand the faiths of others and how that impacts how they might act their daily life and how she can care for them. I think it's really a big driving force for her is where are they coming from so I know best how to care for them. I wish everybody in this world approached faith like Caroline did. We'd be in a lot better position as a world if they did. Caroline, that's really special work. Is there anything else that you'd like to share with the North Texas annual conference? Maybe this.  I didn't even know I'd been nominated, so this came as a complete surprise. But here's the truth. Youth all over annual conference are doing tons of amazing work, and I'm just one small part of that. I've been blessed by the encouragement of great pastors, laity, faithful parents, and by the awesome youth of this conference. Here's what they taught me. Just do the work God puts right in front of you, and do that work with great love, giving all the glory to God. When you do that, it doesn't make you special, it just makes you Methodist. Thank you North Texas Conference. Thank you Fireman UMC. And thank you Pastor Bill and Pastor Holly for nominating me and teaching me. Just do it.


What's up, everybody? This is Jaspie's 15 bucks High-end flashy basketball mixer random teams. We're giving away a Zion Williamson PSA mint nine Penini Donross Marvel insert. It's the gold press proof So that's a really nice card. We're gonna give away at the end of the break No veteran common ship unless their name is Giannis Lebron Kobe or Luca Of course all the rookie cards inserts all that great stuff ship We got some noir in here spectra mosaic So good luck everybody. Thanks again for getting in Joe's gonna be ripping some packs on the top camera while I randomize the lists after six times So remember the giveaway for the Zion at the end. This is just for the break And we're gonna go six times I We got max down to Sean We will have another basketball mixer tomorrow So if you missed out on this one, you can hop in tomorrow And now we're gonna go six times on the list of NBA teams one two three four Five and I will have a trade window Once I name off all these teams Max you got the Los Angeles Clippers Stephen P back-to-back teams here Cavaliers and the Dallas Mavericks Sean back-to-back magic Thunder Scott B. Lakers Tyus Rockets Chris 76ers Michael Bucks Nick Raptors Brian wizards Colin Phoenix Suns Matt Grizzlies Robert Warriors Michael T. Kings Asa Spurs Barry Nets Sean T. Wolves zoom in pistons Adam Celtics Tim Tyler from the was a Xello 169 gets the New Orleans pelicans Summon with the Pacers round with the Knicks Sean with the Nuggets Nancy with the Bulls drew with the jazz max blazers Daniel with the Hawks Also with the Hornets and Sean with the heat So there will be a trade window. I'm gonna leave the video running though since Joe is ripping packed That we will dive into once we see if there's any traits Sam says I love it when a plan comes together. What was the the plan did I miss something there? What was the Sylvester Stallone movie where he's with all like the badass guys? That wasn't a team that was like It was like it had an older cast, but they were still they were like former secret agents. Yeah, I didn't like that It was really bad. It was like that a boomer death squad No, no No, I did well they did sequels. I didn't the expendables expendable. They're doing a fourth one coming out. Yeah, I Didn't like it. I think it made a lot of money, but I don't know if people like that And it's a nager and Dolph Lundgren Jet Lee Jason Statham's in it Terry Cruz, Randy Couture, Wesley Snipes, Mel Gibson Chuck Norris, Harrison Ford, Bruce Willis, Antonio Banderas, and then they just thrown like Rhonda Rousey Liam Hemsworth They're coming out in 2021 the expendables a Christmas story. Wow a Christmas special That's that's like jumping the shark Anybody you want to trade? Drew Kay has the jazz for trade. Asa, Spurs and Hornets up for trade, Max, Clippers, and Blazers up for trade So we got you know five teams up for trade right there Maybe one of y'all want to trade one of those teams for another team and we could put it in our document here And you can go on our way with breaking it. Let me know Did they remake the A-team recently? Didn't they do one with an all-female? No, that was oceans That's oceans too. I Saw the oceans all women. I didn't think it was this bad is what I don't think you got good reviews I thought it was okay They did it in 2010 Liam Neeson, Bradley Cooper, Jessica Beal. That was a bomb. Although it made a lot of money Yeah, here's the Zion. Well, there's actually a lot of trade action, so I'm gonna leave it open still There's a Zion PSA 9 even if you have a terrible break Could win that that will make it all the worse. Wow The marvels You could kill it Ryan says any interest in the Knicks max says I'll trade the Clippers for Knicks Ryan Also says Knicks for maybe the Spurs or Hornets So let me know if not. We're gonna close the trade window here in a sec Also says Knicks for Spurs actually Knicks for Spurs if you wanted to do that So Clipper a lot of different years in this first. Yeah, we got 1718 1819 1920 Remember teams like the Nuggets all of a sudden are a great team to get with bullbolts card surging So you got to think, you know, maybe if you didn't get a great team right now Some of these teams are gonna be in the bubble. They could be having some guys surge in price the next week or two All right, we are done on trades Ryan's gonna decline. So we're gonna close the train to a window Maybe some tried to trade couldn't trade luck for some folks Who wanted to trade? DJ Fluker NFL says his girlfriend punched him That's some news in the NFL going on what DJ Fluker girlfriend punched him No, Nixon Spurs was declined Asa. All right, here is the list of teams Max is asking who he should look for on the Clippers or Trailblazers. We got Nassir Liddle for the Blazers this year There's like some of the higher-end sets you might have quite a lot of opportunities Damien Lillard is in Newar Mophandu Cavangale Maybe some Landry Shamet SGA might be some of the Clippers Yes, Shagel is Alexander. His silver prism is like 900 bucks. Was he 17-18 or 18-19? He's 18-19. So it could be a boot. A couple 18-19. So Clippers are pretty good. Taco Fall is a pink camo. All the pink camos ship only some of them get flea, some of the bigger names Oh, yeah, only the only vets that Vets commons that ship will be LeBron, Giannis, Luc Adonis in second year and Coby, if any, if he's a base card, he exists. Obviously all veteran inserts will all ship. A hero? Yeah, after any Simmons or Simon, there's R.J. Barrett pink You got any sleeves right there? What do you kind of? Regular. Popular or regular sleeves? Just regular sleeves. What's up, Leonard? How's it going? Thank you. Yeah, I accidentally did not put the noir box in the description, Nancy, on the list. But it is in there. But it's in the mixer.  Yeah, so I mean, all these teams with three years, all these teams have some rookies to chase, definitely. Had a good game. I think he had six threes last night, LeBron. I think he went like, yeah, six for six or eight for eight or something. This is Ion NBA debut. That's going out to New Orleans and Tim. And there's a Luca base that'll get shipped. Brennan Clark Green. There's a Silver Holiday. J.J. Reddick Green. Mike Powers saying Montrez-Harrell left the bubble for the Clippers. Yeah, he did. Sort of like Lou Williams. Yeah, I mean, at least the Clippers left. Ooh, look at this. Genesis. Wow. This is why Mosaic Retail is a hit. You can get case hit stuff that you can only find in hobby in most products. Dug out of retail stuff. Carl Anthony counts Genesis. That's a nice one. Sean with the T-Wolves. But yeah, that's kind of crazy. They said they'll be back though. I think they'll be back in time for like the first, they might only play one or two games. But they're already like, kind of locked in at the two seed. I don't think they have a chance for the one seed, I guess. I think it's pretty hard. I think they might fall to three, actually. I mean, they just don't want to fall into position where they'll see the Lakers before the Western Conference final. Because I think that's all they want. So they don't want to go below four, I guess. There's a Romeo Langford Silver for the Celtics rookie. There's a LeBron Evie piece for the Cavs. Yeah, right now in the Western Conference, Clippers have 44 wins, 20 losses. Nuggets have 43 wins, 22 losses. So Clippers only a game and a half up on them. There's a Yanis Green, that's nice. And Utah has 41 wins, that's the next closest team. So they just don't want to fall into like that four or five seed. Where they got to play like Houston or OKC in the first round, and then the Lakers in the second round. That's pretty tough. There's Will the Win, Anthony Davis. Gorn this Angels A's game here. 1-1. I'm going to check. I think it was the 6th inning. Jimmy Butler, Max Monk who has two homeruns. There's Demarda Rosen. Top of the 7th now. Simmons grounds out. Oh, he threw it away? Oh, did he throw it away? Nice, yeah.  Jared Allen? The foul ball thing. They got like 100 yards worth of foul ball territory more than the next stadium. I don't know, now that the Raiders... Like right there would be three to four Rosen. Raiders aren't there, it's like doing what they want, right? I would imagine. They're sort of doing like arena football or XFL. Well, I think they're getting used to it in like three or four years. Just trying to grind this up. It's Dominique Wilkins. How would you judge the centering? Well, the centering would be like, you know, for like this card example, the NBA D&B Utex, the rookie card in the logo box, the name here, the team name, the gate. They look at the back too? Yeah, they look at the back and stuff as well. Obviously, these are kind of harder to tell than like a prism card or a pocket that has borders. Boops, contenders, fast breaks. All right, so we're going to do some 17 team fast break. Those are both boxes. Back in the day where Luka Donchich was just a young guy playing in Spain, and Zion Williamson was playing in his high school wherever he played. Where did he go to high school? I don't know, actually. Is he from Louisiana? No, that's where he plays. That's where he got drafted. North... Is he from the Carolinas? Carahio saw? Salisbury? North Carolina. Ah, North Carolina. That's why he went to Duke, I guess. Jamal Murray. There's a Markel Foltz. Some of these cards do have a natural curve to them. Coming out of the pack, FYI. Was not done in the mail. Champ is here, Kevin Durant. How do you grade corners? How do they grade corners on cards without corners? Like jambalaya cards.   They have the grade all eight corners. But yeah, like the jambalaya... Ooh, look at this. Jason Tatum fast break rookie. Ooh, cool. Parallel there too? Nice. You guys are pulling too much heat. We need to take that Jason Tatum right away. It is too hot. Adam Kuperman with that one. Too hot. Um, MTG says hello again. I've always wondered if the curve affected grading. I don't think it does, no. Unless it's so bad where it's like, affects the corners or something. Just kind of straighten it out, right? Yeah, and like once they put it in the... In the... In the case. In the case to case? Yeah. Oh, LawyerServiceDirect.com says I'm from the next city over. It's pronounced Sausberry. He played at Pride of the School in South Carolina. For high school. The Sausberries taste like Sausberries. I was thinking Salisbury. There's another set. Yeah, the Salisbury today I guess. That recent Jason Tatum sales $256 $155 $125 $175 $324 All raw prices. So Adam K who got the Celtics in a spot filler is already winning. There's John Collins. I like him a lot. Wayne Bacon. We've got a redemption. Anyone want to guess? There's a Siakum. $130 out of $155 one of the more underrated players in basketball. Pascal Siakum. Has the Raptors in a position to get the two seed right now. When no one when everyone thought they'd be bad or not bad, but not as good without Kauai. Because they're like there's Bacon a $109. Few games behind the Bucks with a one seed. Yeah, I mean they're out there well. I think everyone thought it was going to be Bucks, Celtics. I mean they got 46 wins. That's more than that's more than 2017. They're only a couple games behind the Lakers. If my Lakers don't get to the finals I would like to see like I'd like to see like Clippers Raptors battling the old team. There's each one more for the Pelicans to 50. I don't know if Adam Silver wants to have that. Jack Sportsbreak says we just pen in the mixer. Thanks so much. That's never leaving my collection. Oh nice. That's awesome. Congrats. There's Zach Collins. Pat Beverly. Sean Marion. What do you guys hair like that? I kind of want to dye my hair. Yeah. Go for it. Trevor Booker to 193. Like Kyle Puzma. This is the redemption is Kevin Durant. That's my only guess so far. Zach Collins. What year is this? 1780. There's Wilt Bestill. There's a red Ryan Anderson. Number to 85. I feel like it's someone random. There's Bam Adebayo. Who I think just joined the bubble a couple days ago with Kendrick Nunn. The Buble. Yeah, the Buble. The Michael Buble. Two boxes of Optic with Teddy. And both were hot boxes. Wow, nice. That's pretty good luck. Here's a nice one. Rookie Autograph. Fast break signature is John Collins for the Hawks. That's Daniel Grant. And there's a blue Al Horford Celtics edition. Number 155. There's a Donovan Mitchell as well at the very end. So almost got every, I didn't say any Lonzo. I wasn't him. Got pretty much every big Sempani to Rookie. Those two boxes. Alright. Let's see what the redemption is. We got a rate of Rookie signature. Fast break. Timberwolves. Part 152. D. D-I-L. It must be Dillon Brooks. Grizzlies. Yeah, Dillon Brooks. I believe it was a Grizzly. Memphis Grizzlies would be Matt B. I think he went to Oregon. Mercury. Yeah, that wants to go. The Mosaic Hobby. Correct. Alright, we're back on the Mosaic Train. Maybe we'll see a stained glass insert in this Mosaic Hobby box. Which go for tremendous amounts of dollars. Alright, so I'm leaving Isaiah Roby, red. Choice War box for you. I cut the stickers on the war. These are high end enough for you. Slow play though. Everything else is open. Boom. Overdrive. Yanis. That insert sets nice. I like that. Milwaukee Bucks is Michael M. Hall of Fame. Dr. J. Stairmasters. Blake Griffin. There's Alonzo. Grayson Allen. Terence Mansilver for the Clippers. And we got a pink. Number 49 Tremont Waters for the Celtics. Yeah, I like the Mosaic a lot. It might be my favorite product this year. In its win at Ben Simmons. Nikhil Alexander Walker. Dirk. Not a number. I don't know. I haven't been into a Target or Walmart maybe once since the COVID hit. Paul George. I'd imagine they're still pretty empty. Maybe less empty though. 25 Ladi Divak for the Sacramento Kings. International Man of Mystery. Serbia. And Nancy, I think you're lagging because I think you might have hit the live button. You just respond in. Oscar Robertson. There's a Korean blue number to 99. Center stage. LeBron James. Very nice. Center stage. LeBron. Right behind him. Zion True Rookie Base. That's one for the Pelicans there. Redemption again. See who it is. Any guesses on that redemption? Mosaic, basketball, hobby. Hachimura. Tremont Waters. There's a Montage de Rosen. COVID White. Good luck. We have a Rookie Autographs Mosaic. Card 5. J-A-X-S-O-N Hayes for the Pelicans. That is for Tim Tyler. We're going to do some 1819. Pups in the park. Dog cutouts. I thought you were going to say the owners can drop off their dogs. Just have them run around. And then come back. That would be so cool. Big dogs taking the big dog part. But no humans. Only dogs are allowed. That would be so cool. I think Mookie Betts and Cody Belanger are going to be flying around there. Spencer Dinwiddie. Hot signatures. Who's that? Deeter Downs? You can't pay me enough. Who is that? I've never seen that face. Jamal Murray, 9 of 99. That must be Terence Gore. Not that I think about it. Well, not Terence Man's The Clippers. Terence Gore. Jared Jackson Jr. This game's over. Mookie Betts at the base. Kareem. You might see an extra innings game in this one. There's a Picture Perfect. Donovan Mitchell. Not numbered. We have a Josh Akogie. Mike Towers said you could attach a GoPro to Bubba and a microphone. We could live stream it. We could have a paper view. See what kind of antics Bubba gets into at Dr. Sadie. With no dad there. 95 out of 199. Bill Roswell.  Oh my God. Rosin all over the place. The mask on his face would be all over his ears. His velvet ears would have all sorts of Rosin all over. Sticky from the Rosin. Walker Bueller running around. Pulls a hammy trying to chase him around. I like this insert. Archaeologists. That's pretty close to that text. I guess it's you can't copyright a font. I thought you could. We named the dog Indiana. I've only seen the shy of the buff one. What? 14 of 199. I believe it was for all these failures to see like plastic. Turn out right? I like the shy of the buff one. People hate on it. That was terrible. I thought it was cool. Ray Allen. That's the first one you've ever seen. You probably think it was cool. They had the theme song in there. No Luca. What the heck? The 2018 Al Horford. It was looking for a Luca to not get one. Did get a Trey young but sexed him. The end is 1718. There's a Yanis superstars. Robert Oriotta for the Lakers. Big shot. Robert Ori number 25. Shaquille O'Neal. That's not numbered. 101 printing plate of Ricky Rubio for the Jazz. I was going to say Ricky's 10 house junior for a second. Utah Jazz on that one. Aaron Rodgers and Danica no longer together. Danica's on the market. Hassan Whiteside. We got a Contenders Optic Season Ticket Short print. Zach Levine. We got a Wesley Owendu auto on-card number to 65 for the Orlando Magic. That's going up to Sean N. There's a Manu. There's a Marc Gasol number to 249. Edgware on the bottom there. Dwight Howard. Season Ticket K Love for the Cavs. A few more boxes to go. Until the high-end stuff. We'll do this Optic Mega. Yeah, I've seen that Zach Levine is not happy in Chicago. I've seen him with Lori Marketing. I think might have requested that trade too. There's Kareem. I'll see her little. Well, those Contenders Optics, I just know that are short print because we've ripped so many. There's only like one or two a box. There's no way to really tell though, but at least on that design if you're opening like tenders, you can see the shininess on the left and then just the paper on the right. There's a Hollow Ignace for the Knicks. Kauai. Hollow. Yanis Pink. Taco Fall. For the pinks. Omega.  Let's do Chronic Hanger. This is a quick box. Kevin Herter Green. Michael Porter Jr. Bridges Obsidian. There's a Luca. Just a playoff, but still. A Luca Rookie. Jalen Bronson. Chronic Hanger. 1718 Chronicles Hanger. Sorry, Chronicles Hobby. There's number 199. Rudy Gobert. And is this autographed? It is. Rookie Auto. Number 49. Donovan Mitchell. Utah Jazz. Drew K. Nice one, Drew. I think you might have the Jazz for trade. So there you go. Number 49. Donovan Mitchell. There's a BAM out of bio. Number 49. There's number 299. I hate when they have numbers on the back and numbers on the front. Zach Collins. Numbered. Lori Markinin. Not numbered. There's number 149. Kent Baysmore. There's Devon Reed. 14 of 199. Gralic Auto for the Sons and Collins Smith. Harry Giles. 99. Jonathan Isaac Brilliance. Jonathan Newby. Patten. There's number 99. Andre Drummond. And there's Terence Ferguson. 99 of 99. eBay 101 Relic for the Thunder. There's John Evans. Number 249. Tony Bradley. Number 149. There's Alonzo. Majestic Rookie. That's nice. That's Chronicles Hobby for you. Let's do... 1718 Prison Rose. Josh Jackson. There's a Tatum. Nice. Jason Tatum. That sounded good. What happened? Camera... What the heck? Warning track power. Dude, that would have been a home run if they kept it on. Come on ESPN. Did you hear it though? It sounded... It sounded real nice. Nice Tatum there. Adam Kaye. I thought there's Otani's MVP campaigns. There's a hit today too. Is he pitch writing? Bradley Beale to 99. Or does he throw lefty too? I'm blanking on that because he hits lefty. He pitches righty. He's an... Amphidextry. Is that how you say it? Amphidextrous. Does that definition apply? Yeah, I think so. I think that's only if you could hit... Well, I guess... There's Alonzo. There's Giannis. Is that Collins? LeBron James. That's a nice run. Kawhi Red. Devin Booker Orange. And Dario Starfish. I just want to see what's in the rest of this. I was about to leave and I was like, wait a second, it's pretty close. Otani throws right, yeah. What kind of throws right? He's not Amphidextrous. You would have to throw with both arms. So what is it called when he bats lefty, but throws righty? Is he a switch hitter? Maybe he's just a switch hitter. No, that's if you hit left and right. I don't think he hits righty. Does he hit righty? I don't think so. Frank Niloquina, 7 of 185. I missed how they scored a second run. There's LeBron. I think I was watching... You said the dogs in the park and that... I switched the channel for a few minutes. It was just like Banfield Pet Hospital. Oh, Frank Mason, 505. Rookie for the Sacramento Kings. He's considering Dodgers. I think he's a South Bay Laker. This is Kings. That is Michael T. They don't call him. They've got to have a name for that. Yeah, if you hit one way, they've got to create the name. We need to create it right now. It's a 25 Aaron Baines tie-dye. It feels like a really big park. That A's park, doesn't it? It's so big. There's Harrison Barnes on card. Dow's Mavericks edition. What is it down the left field? It's like 400 feet on the left field line. It feels like... I feel like in L.A. I feel like in Anaheim, that ball would have gone out. The Otani hit would have gone out. Alferucomino. Another Jason Tatum rookie. This is the premier level. Nice. Kauai Silver. Brooke Lopez Lakers edition. Relic, you get there for Scott B. Josh Richardson, blue. Number 299. Number to 65. Relic Auto World B free. Philadelphia 76ers. That's Chris Erickson. Would the world be free? 32 of 65. Wow, look at that. Jason Tatum Silver. Jason Tatum Silver. Geez, what a break for Adam. Does it have a level on the back? Yeah, this is the... Uh... It doesn't have a level. I think it's Concourse. Concourse. Concourse Prism Silver. Select. Rookie. Tatum. What does that go for? And there's Archie Diakono. The top, the leader in the clubhouse right now as far as the value. What are you looking at right now? Yeah. We'll do Spectra. We'll do, yeah, it's about two... So, BJ is 9-5, so for 600. And then the raw one goes for about 250. It's pretty good. My first look at this year's Spectra I haven't ripped any, so let's see. Actually, I did rip. I don't know what I'm saying. We got Andrew Wiggins, Golden State Warriors. 49 of 99. Drew says batting and throwing opposite is called Cross Dominance. Cross Dominance, nice. Nice poll. That's a good one. Robert R. with the Golden State Warriors. What's up, Adam?  Kai Jerome. Number 25 Thaddeus Young Auto for the Chicago Bulls. Theoretically, it provides more power. Drew says. Chicago Bulls. That's Nancy. Number 25. There is Drew Holiday. Number 99 Celestial. Celestial. Drew Holiday. Pelicans. It would get more power if you throw right-handed. Kai Bowman. If you throw right-handed. Yeah. That's what Drew says, quiet. So you're... Ersan Ilyasova, number to 75, would be your lead arm if you're getting lefty. There's more power that way? You guess you're not. Yeah, it does sound like that. You're on camera while demoing this. No. Yeah, I did too. I remembered when I sat down. But then I forgot about it. Would you lead with that hand? That might be the one that holds on to the bat the longest. More follow-through. There is Aaron Gordon. That one's number to 49, Interstellar. I hated that movie. I hated it. I thought it was so overrated. Kuzma. You like that better or Arrival? I hated Arrival. No, I like Space Movies. What kind of space movie do you like? The one sex in Star Wars. In the Zone Auto. 55 and 75. That's a good space movie. Cleveland. That is Stephen P. Although I don't really like the ones that are popularly liked. And there's the 99. Nick Claxton. What do people say, number one is a new hope? I didn't really like the new hope. Like the prequels? No, I like Revenge of the Sith. That's not a bad. That's probably the best of those. Yeah. The Martian is a great movie. With Matt Damon. I have not seen that actually.  I haven't seen that. I do like the space movie. That's a killer movie. Is that a spoiler? No. I'm just thinking of adjectives. Chris Paul. Devin Booker. Jamal Murray. Alexander Walker. Number 250. Atomic LeBron James. Nice. 35 of 50. We got to sell out that obsidian tonight, guys and girls. There's two number of blocks left. I'm probably refunding the obsidian by Sunday. That's been up 12 days. I feel like it's so... I know it's pricey, but it's also... Scott, there's so many hits in it. Yeah, there's tons of hits in it. We're going to spend their money on noir. Matrix Auto? I know. But that obsidian is really nice.  That might have been a problem. 35 of 35. People loved it. And we got Jalen Noel. Autograph Relic going after the T-Wolves. 42 of 75. The weirdest thing is baseball players that play golf opposite than what they bat. I feel like that would eff up your swing. Would they do Oppo because it would eff up their swing? Yeah, maybe. That kind of makes sense. My tennis coach said I wasn't good at tennis because I played baseball my whole life. He didn't say I wasn't good at tennis. He just said why I'm not catching. You're upper cutting. You're at launch angles. Yeah, exactly. All right, we've got Mafandou Cavangale. Quendari Witherspoon. Grant Williams. Eric Pascal. Michael Alexander Walker. Kevin Nox in 99. Mafandou Cavangale to 35. Let's go with choice. Autograph Daniel Gafford for the Bulls. Volleyball Nancy with that one. Remember, if you're not having a good break, we still are giving away that Zion PSA 9 card at the end to everybody. Deandre Hunter-Auto. That's a nice one. 77 of 99 rookie dominators. And we still have a whole box of Noir here. $1,300 box. So I've still got some time to catch up. Vanilla Grill says that Obsidian Lebron. I just pulled once over a thousand bucks. See? I don't know. It's like it's underrated. Was that best offered? It's a lower price point than Noir. But I feel like with higher margin for what, you know what I mean? I feel like your return can still be a higher margin. Right. This game's going to be in overtime or whatever they call it now. No, remember they're going to put a man on second so it'll be like over quick. I know, but what if they both score? What if they keep scoring? I mean, yeah, that's the thing. D-Turk says the orange out of 35 was a thousand. Still nice. Still at least a few hundred bucks, right? Yeah, four, five hundred bucks. Yeah. Cam Johnson, 12 out of 25. That'd be awesome. And Kevin Knox to 99. Anyone bothered grading these more? No, I don't know. I don't know if it's because of the box.  Yeah, those things are always a mystery. Especially if it's black. They should just pack it like NT, though. There's 43 of 99, Tyler Hero. I feel like someone got fired. You know what I mean? Like some box manufacturer lost their contract. It's just so smooth with the boxes. Car slide out perfect. There's a Lori, 91 to 99. Jumbo material. We got Andrew Wiggins, T-Wolves, uniform, number to 99. Lucas Samanich, 10 out of 25. New Wave jerseys. Nice three-color patch there for Asa in this first. We got Phoenix Sun, Ty Jerome, 91 to 99. Going out to Phoenix. And Collin? Three more. I don't know if it's a base on the bottom. I don't know. I have to check. Gary Harris, 5 out of 49. Nuggets. That is Sean. No, a thicker card would probably grade worse just because of the corners and edges. They're usually in poor condition. Oh no, so we've got two signature spotlights coming in. Back to back. We've got another one here. First one, very nice. Number to 125, Kevin Porter Jr. Havesteen might be... Yeah, they got rid of their coach. Yeah, so Sneak. Ownership's a little goofy. Steven Peay with that one. I think people think Kobe Altman, I think, the GM. I think they like him. All right, in the last card. Good luck. This is it. Spotlight signatures. It's another rookie. This one's number to 99. Eric Pascal. Autos. Spotlight signatures. In the San Francisco uniform right there. I feel like they're going to trade him and like pool or something like that. That's Robert. They're going to like shine on another team. Yeah, I can see that happening. I think the war is just going to be like wind-down mode. It's going to be nuts. They're going to get the number one pick and probably trade that. They'll get whatever. All right. Giving away the Zion Williamson PSA Mint 9. Good luck everybody. Maybe it could go to somebody I didn't call yet. Or you never know. It could go to Adam with the Celtics. We'll see how things play out after six times. Four and a two. One. Two. Three. Four. Five, six and final time. Six. Sean M. Very nice. Sean Matic with Mosaic Sello 167. Gets it. Had the majority you know there. He had I think three or four spots. Congrats Sean. Thanks everybody for getting in. I'll have another basketball mixer. Oh no. I don't know. We'll have another basketball mixer. Saturday night. 3-2 in the bottom of the eighth and a man on third. Only one out. Thanks everybody.


you can follow along with this presentation using printed slides from the nano hub visit www.nano hub.org and download the PDF file containing the slides for this presentation print them out and turn each page when you hear the following sound enjoy the show all right so this is lecture 5 on energy bands and this is today is a very interesting lecture in the sense that today at least finally will be solving a real problem it's not real yet but it gives a lot of information about the real thing we eventually want to know about so we'll start by talking about how to solve Schrodinger equation in periodic potential UX now remember why we want to solve the Schrodinger equation to begin with because as I said not all the electrons participate in the conduction process equally so if you want to know the resistivity of a material then in that case we'd like to know which fraction of the total electrons are actually taking part in the conduction are available for conduction so in this case we want to know where the electrons sit to begin with and then subsequently we'll figure out what fraction of them moves and the periodic UX well because it's crystal and in a crystal we want to solve the Schrodinger equation to see where energy levels stay within a crystal and then we'll talk about a set of set of other things now this is again the problem that we had been talking about in the last class as well and this is a problem where the red electron is sort of swimming through a series of ions or the core of the nucleus and they are being periodically pushed and pulled by these respective positive charges and the electrons are of course negative so and what we did in the last class in solving the toy problem we assume the atoms are so far apart that we can just take one of them don't worry about the neighbors and just take one of them say where they are if they are very close to the bottom or way up in energy how they transmit and where they stay but of course atoms are not far apart they are only five angstrom apart or less than in many cases maybe two angstrom apart they are not far apart so in this case it is impossible to sort of neglect the effect of the neighbors and that is essentially the essence of this problem that we are going to solve now let's consider this full potential in in a in a simplified way remember again the the reason we write it as a square potential going up and down is because it's an idealization in practice it will be like a series of Coulomb potentials you remember this hyperbolic type relationships and they will one over art type relationships then they will sum up but this is idealized version just for simplicity but it will give us many information which will be correct also in real crystals okay now this is ux goes up and down in position now if you look at the period let's define them a is the bottom of the well so this sort of the extent of the atom let's say and the b is a barrier between them and the period then therefore is a plus b we'll call it p remember this is not momentum this is for this case just a distance you know maybe five angstrom from one atom to another now you see something funny here that I can of course solve for the Schrodinger equation here in one shot if I take an energy which is below ux in that shaded region as you can see then when the energy u is higher than k your energy then you know how to write the solution e to the power alpha x plus e to the power minus alpha x that we have seen in the last class what should we do when the energy is above the potential you know in the white regions in between well we'll write it as sine kx and cosine kx and remember I have to know which white region I am writing at so I put a little index n plus 1 just to say that this is next to n n region so I put an index so you know for every set of pair of this potential there'll be one two three four and so on so forth so I have a series of solutions now if you didn't know anything else then and simply applied what I told you last time that is take a boundary condition and plus infinity another at minus infinity two unknown constants gone every interface match the wave function match the derivative right then you can essentially solve this problem no problem but you can immediately realize that even in a centimeter cube of material even in one dimension they are probably hundred million atoms sitting now you have to solve hundred million multiplied by two equations now the boundary condition may give you two less but that's not really helping you so this is an impossible problem to solve and there's no way then in 1940s when these problems were actually solved you could possibly solve it there is no computer but it was of course all that time and this is how and and what helped the solution of this problem is this beautiful theorem called block theorem will not prove it or anything but just show you the content of the other theorem that how it solves it it's very simple you'll see now remember the four steps there are five steps of both solving for the energy and the wave function the first four were determining the determining the eigenvalues of the energies now we write the same equations but as I just explained in the previous slide that if I just use this rule blindly too many equations cannot solve it and therefore I cannot know where electrons sit what I can do in a state is in a state of using two and three we can replace it with something very simple using the fact that this is a periodic potential it's not any arbitrary potential things repeat and that information we should be able to use somehow to reduce this humongous problem to something that you can solve essentially in 15 minutes now remember where that comes from or see how it comes from so the main feature of this potential is that if you take any given location ux position x and potential corresponding to that ux assuming that x equals 0 is the origin on the left and that can be an arbitrary origin then you can see that when x is displaced by a plus b the potential is the same it's one one period away and I'm instead of a plus b I'm writing yes p in order to save some save some time now if the potential is the same then although I don't know the solution yet I don't know the solution of the Schrodinger equation but I could say this that whatever be the solution at location x the solution at location x plus p must be the same remember the definition of this Bravais lattice and the periodic solid that every point you sit looks around you is exactly the same as every other point you sit now if every point you sit looks exactly the same the solution whatever it is we do not know whatever it is that must also be the same so if that is the same so therefore I can say the probability of finding an electron at a given location is exactly the same as it is one lattice site away what does it say about the wave solution itself the psi this is this is psi squared what about psi itself well psi you can see the wave function is almost the same except I'm allowed to have a phase factor e to the power ikp again p is not a momentum it's a distance why ikp why is the same well if k was 0 no problem right on both sides I have the same thing square it no problem but remember this is an absolute value squared that means it's a complex conjugate psi psi star and so when I have psi star then obviously on the right hand side I will pick up a minus ikp and when I multiply them to then of course this ikp e to the power ikp will go away so therefore the solution on the other proposition on the left hand side that the probability of finding an electron is the same one lattice site apart implies that the actual solution one light side apart must be given by this wave function multiplied by a phase factor you see so take this this is an important step and so you should try to understand that clearly okay and this is although also by the way this is k is not this h square k square divided by 2m as we saw before this is just a number k because k could be anything I could multiply with anything and when I multiply with complex conjugate anything I put it will always go away so k doesn't have to be any specific number it will be in a second but that's not the old k okay so now let's use this information see how it works I just told you that if I know the solution psi x at any point if I knew then at x plus p distance away the solution will be related to each other by the relationship shown in the bottom you can see at x plus p this simply one phase factor shifted for the original solution at x well if this is true then isn't this true as well if I wanted to go two step not one then the second step I could relate back to the first step and I could write that psi at twice the step is simply psi at the first step multiplied by the one phase factor right you see this and if the first one is already known from the left-hand side you can see and therefore this I could write do you say this that when I have gone two steps I could in sin in cascade the solution back and essentially pick up the phase so if I am to step away I will have a pick up a phase factor compared to the first one 0th one is by 2 kp so you can see that if I am n step away and n could be a billion if I'm n step away I don't know anything else but obviously I could say this n step away this statement should be obvious because what I'm doing here you can see I have picked up a phase factor which is kp of course but now multiplied by n so I have n phase factors and this you can see where it came about the n was connected to n minus 1 n minus connected to n minus 2 all the way folded back until you hit one and that's where you picked up all this phase factors well I haven't done any solution yet but simply I'm setting up the problem and in a next three or four slides we'll see how to solve use this information to solve the problem this is something replacing the boundary conditions you see continuity of the wave function and the derivative of the wave function that is something we'll use on top of this equation now let's look at this and then say the following statement now this part is not obvious and this is sort of one of the tricks and we'll see how it works but I'll explain it later on so assume you have taken this string of atoms now you pull it back now how do you pull it back in real crystal you couldn't possibly take the atoms and pull it back in a string right so in principle you couldn't do it but what you are telling here is that when the atoms are so far apart let's say one and a million unless the atoms are very close to the surface in between you know one side you have a million plus 20 another side you have hundred thousand or something it really doesn't matter what you have at the very end because it's so far away so therefore whatever you do pulling it back twisting it whatever you do it's not really going to change the solution inside of course we are not going to know that unless we begin to compare it experiment later on that whatever we did this is correct or not but for the time being we'll proceed and then we'll come back and see whether the solutions are real or not now if I pull it back then what will happen you see so I'll start from one two three go all the way but now the n minus one the nth one is again the first one and then two n one is again the first one you see so this because it's a periodic boundary condition that's what they say in that case what should happen well in that case you can see that if the nth one is exactly equal to the first one then psi x plus np should not be just a phase shift away it's the original thing because on the left hand side I should be able to replace this with psi x again because it's the first one and if the first side left side and right hand side has to be equal then you can see then e to the power i k p m that must be equal to one only when I pull them back together and if it is one then you know that this one equals e to the power i 2 pi n do you know this formula this is so this is so I can set these two things equal because every time something is twice the multiple of pi 2 pi and when it's to the power i and in that case the result is always one you know because it's like 360 degrees coming back and coming back again and so I can write k equals 2 pi n divided by np is this true do you see that if you look at the exponent on both sides left and right and divide both sides by np then you can see that these solutions are correct it satisfies the solution what does it tell you what it tells you is that any arbitrary value of k is not allowed if the potential is periodic remember the phase factor I had e to the power k p now any arbitrary value of k will not work if it has a periodic boundary condition then it must have 2 pi n divided by np now little n it could be 1 2 it could be minus 1 all the way to n over 2 why could it not be n plus 1 over 2 you can put it over there and you can show that that's exactly equal to 1 1 again the value is 1 again another thing I want to point out that there is this solution of the k that has two sides positive sides 0 1 2 3 4 and the negative side 0 minus 1 minus 2 minus 3 so on so forth what does it mean the plus 1 means remember e to the power plus ikx wave going in one direction right positive direction e to the power minus ikx was what was it wave going in the other direction so this is like wave going on the ring in one direction that's e to the power ikx wave going in the other direction e to the power minus ikx so of course both traditional solutions are fine electrons could go in either way and that's what the positive and the negative strings mean okay so we are getting there not yet but getting there remember any arbitrary value of k is not allowed only certain values of k are allowed okay what is the maximum and a minimum value well we can see what is the maximum the maximum would be when little n is equal to capital n over 2 and if I put it over there in the equation I will see pi divided by p and on the other side minus pi over p that means all my solutions whatever they are cannot exceed this boundary I don't know what the solutions are but it cannot exceed this boundary and later on we'll call this brillouin zone because this is where all the solutions of the eventual equation this is where they live okay now finally we are able to solve the problem let's see how it works do you remember the solution that I have on the left hand side of zero zero to minus b sin beta x and cosine beta x now on the right hand side between zero to a few slides before what did I write e to the power alpha x plus e to the power beta x right minus alpha x remember I'm here instead writing in terms of sine and cosine is this right well if it is at if this is equal to a imaginary quantity then it's fine sine and cosine will be fine if we write want to write it e to the power alpha x in the with the exponent alpha and beta in terms of imaginary it could be real or imaginary in that case writing in this particular form should be fine you should check this out just by inserting the equation that you know you you see the definition of alpha and beta above you should check it out yourself that this is exactly the same as I said before in terms of e to the power plus alpha x and e to the power minus alpha x exactly the same now let's use the boundary condition first on the green line or the blue line I'm not colorblind yet but so the blue line and what do I have to solve here match the boundary condition I'll have to say wave function is continuous and its derivative is continuous right okay so I know the two solutions I should be able to do it in a second so at x equals 0 minus and 0 plus I can say the continuity of the wave equation and its derivative and I will not labor you with this statement that b sub a equals b capital b sub b because you can see if you insert x equals 0 in this particular equation and let the wave function be continuous that's the relationship you're going to get okay the other thing is well then I should have to go to the other side because now I have to match the boundary condition at x equals a then I will be done but you can immediately see there is a problem if I need need to go to the other side from 0 to a and need the information from the other side then in order to know that the information at a plus I will have to then solve the next way atom then I'll have to solve use that information in order to get that information I'll have to go to the neighbors and I'll have to keep going to the right now this is not good what I want to do instead is the information we just collected that the wave function at x equals a what is it equal to the wave function at x equals minus b right one lattice vector away right except that there's a phase factor remember this is a periodic potential so it's not exactly equal up to a phase factor it's equal so instead of looking at the right I'm looking back within the unit cell itself this is why you read unit cells spend some time Bravais lattices and everything this is why you do it because then we so once you know the solution within one cell you know the solution for everything for bulk of the material okay so I want a slightly right to the a and that's equal to exactly equal to something slightly right to minus b that wave function within my same cell and therefore see whether you agree with this statement what I wrote that psi at a at x equals a meaning a minus a little bit to the left is equal to psi b but see the phase factor e to the power ikp and why is that because I have folded it back one lattice psi I have that equation and of course I have the derivative equation the derivative equation again has the little phase factor sitting there I'm actually done with this because I know the wave functions I can put them in you see on the right hand side the first equation on the top capital a sub a sine alpha a plus capital b sub a cosine alpha a this is simply by inserting x equals a in the solution of the above equation in the well region and so on so forth you can you can just match it up please take this time when you go home to take this out I'm going very fast because this is simply algebra it's not the conceptual point that you need to know but check it out whether it's correct I have how many equations do I have here I have four equations right two blue two red how many unknowns four unknowns you can see b with sub a and b a with sub a and b I'm done actually so if I have that the step four was put them in a matrix if I put them in a matrix then how do I find the solution of the eigenvalues I make that determinant of this matrix equal to zero and this is a simple four by four matrix how difficult can it be people could do it in 1930s and we are more sophisticated right so we should be able to do it in a few minutes and when you do you get a complex looking equation like this but just like when we solve for one quantum well problem it's no more complex than that because you can see in this equation the only unknown is xi and xi is essentially e divided by u0 u0 is already given from the material that we have and there are of course lattice spacing involved there is this a involved in various places that is something we also know so the only unknown in this equation is energy level e and once I solve it then I know where the electron sits in a crystal and how can I solve this again two ways you can solve it matlab but if you are not in matlab age you can solve it graphically as they do in the book and let me show you how to do it in graphically and that's where the band structure will come in so band structure is the solution of the Schrodinger equation in periodic potential so that we know where electrons can sit not necessarily they will sit there but we will see where the electrons can sit there's a distinction there's a distinction between a chair we are calculating how many chairs we have sort of in a room we are not still talking about what fraction of them are occupied you know so that will come later and so right now we are just calculating the solution of the Schrodinger equation all right let's talk about the band structure this we should be able to do and if you please pay attention to this one because this is where people generally miss it so let's first plot the right hand side remember we'll plot the right hand side and the left hand side look at the intersection let's plot the right hand side first remember that p is given that is spacing and k has discrete values 0 1 2 3 and corresponding to that 2 pi n divided by np so when k equals 0 what is the right hand side cosine kp is 1 and that 1 does it depend on energy 1 is 1 and so with k equals 0 I should draw a straight line independent of energy because it doesn't depend on energy what about k little n equals 1 well I should then have 2 pi divided by np right n is the number of atoms in this string and then I should have a solution that's again independent of energy but goes straight all the way through now you realize first of all that this one would have also been the solution had it been n equals minus 1 because cosine theta equals cosine minus theta so wherever the value is a little less than 1 but that's straight independent of energy right I'm just plotting the right hand side you can see the right hand side is actually how many equations this is n number of equations so right hand side is n number of rate curves actually it's not just 2 n number of rate curves okay I'm let's say I'm done I have spent a lot of time of course you have to draw how many lines maybe a billion lines but don't try at home this is one thing you few lines would be fine what about the left hand side well left hand side is a little complicated but you put it in a any graphing graphical routine you see that it will go up and down as it as it moves around in energy but this time of course the function of xi and xi is a function of energy so therefore you can see there is oscillation in energy where are the solutions solutions are where the rate cuts the blue because that's when the right hand side is equal to the left hand side so I'm done actually I'm done solving it I'll just have to read off the numbers in a particular way what I have done simply is rotated it 90 degrees just like we did in the last class remember rotated in 90 degrees and let's look at the solution then so this is k equals zero right this blurred this red line the solid red line is k equals zero and so I'm drawing something with energy in the y-axis and the x-axis is k so those are the first two points that cut not really the first the ones that I show in the dotted line as the second and a third you can see there is also a point that cut is below which is the first point here very close to energy equals zero okay so this is my solution at k equals zero for all those electrons that has k equals zero actually has these energies fine now what about the next solution remember I have the next line also and from cutting from that next line I will pick up a bunch of solutions there also so I correspondingly shift it to the right and again blue blue cuts the red dotted line now this time what is the value of k the k value is 2 pi over np so on the right hand side right hand figure instead of plotting it as a function of k equals zero I should shift it a little bit and pick up those points that is 2 pi divided by np do you say this that that will also give me a bunch of solutions now remember k equals plus plus k and a minus k gives me the same solution is that right so therefore if I go to the left side on the right hand plot I will pick up a symmetric point on the other side just like the first point pick up the symmetric point and this I can continue how many maybe a billion times I will not do that but you can see that if I kept doing this then I will have a bunch of solutions and these are all these red dots now one thing you will see that I have connected the red dots with the black line why did I do that because black line means a continuous that for all k values as if there are solutions but actually not right for red points are discrete these are not a continuous line the reason I can do it is when you have 2 pi over a billion n n is a large number and when you have 2 pi over billion plus 1 then essentially these are so closely spaced that even with a microscope you cannot probably see they were part so they this red lines essentially look like a continuous solution and therefore many times you will see that they are joined together people don't put this little dot points they just simply join together as a continuous point now what is the right hand side maximum right hand side of this k remember it was pi over p maximum k max and k mean so all the solutions stay live in this space and that's why the in the x-axis will call that region the k region is a brilliant zone associated with the solution now electrons can sit in many places I see but there are also places where electrons cannot sit you can see okay now how many solutions now I'm going to describe to you we have them done we are done with the solutions we could go home but rather is let's stay with it and try to understand a few features of the solution first thing is how many dots do you have in a given band what is a band well a bunch of solution which are together you can see how many banks we have we have four bands of solutions in the bottom second third and fourth and you can see each is separated by a certain gap we'll call that band gap it's a band of solution separate by a gap so therefore it's called a band gap and you can see how many solutions do I have let's try that so remember number of states per band how many solutions I have so I'll have to take the maximum region k max and the left hand side minimum region came in k max minus k mean is you can see 2 pi over p do you see on the bottom side for the graph the maximum side is pi over p shown here in the red and the minimum side is minus pi over p shown in the blue so the difference is 2 pi over p and 2 pi over p but the delta case where the solutions are available is 2 pi divided by np and therefore if you divide it up every band has n points you see so how why did it come about well remember that every atom there's let's say once you remember in the square potential I had first bound level second bound level third bound level when I bring a lot of atoms together these bound levels essentially all mixed together if I have n atoms then I have contribution from nn of them and so per band per band therefore it gets n fold degenerate right there are n solutions per band it is like potlack you know you can have let's say you do your own cooking at your home but if five people get to the potlack and then naturally what we'll have is five five different type of dishes right and if everybody prepared three and then you bring them up all together and mix it up then you can see for each type of food let's say the entrée and the desert and everything each type of food you will have five fold if you had 20 friends then you will have 20 of them if somebody if everybody's really cooking and it's the same thing now if you had to solve this Schrodinger equation every time you would be in trouble because that will be a lot of work and what we'll see that down the road it's actually not we don't really need all this information different people need different pieces of information for example remember the photoelectric experiment light coming in kicking an electron up and the electron coming up they shine x ray on it let's say so in that case i need to know the bottom level all the way to the vacuum level how far they apart all the gaps and everything i need to know in that case i really need to know the whole band structure but many cases in transport you will see when the electrons are really on the bottom side they don't really participate in conduction so for us many times we don't really need to know all of them just the ones that are relevant so we want to capture the information that is in over there into simpler things so that we don't have to carry over this all this information so that's what we're going to do now and that's the properties of the energy band from an electrical engineer's perspective not from a spectroscopy's perspective so let's take the question we want to ask now in the next four or four slides or so is if our electron was sitting in a band and i applied the field or i let the electron move what velocity does it approximately move with that's what i wanted how do i do that well i know the solution at every point and its neighbor so i write it as a e to the power you can see as an exponent i k x and minus i omega t what is that i omega t remember there's a plane wave with a given k that wave is moving if i put at one level that's the plane wave i will have at that state let's combine two of them so one is in red another is in blue on the top the first one is at k and the second one is slightly higher at delta k apart now when i put them two together what will happen since their k is not the same their energy is not the same they will interfere each other it's like two lights with two slightly different wavelengths so they will interfere with each other and when they do let's say the red one looks like this there's a plane wave right at a given time that's the snapshot and the blue one looks like that why because the wavelength is slightly different right the k is slightly different wavelength is slightly different so therefore even if you started them off both at the same point they will not stay in sync and therefore if i combine them it will sort of in one place it will look like it will interfere constructively and in the rest of the places it's going up and down all the way and so it will gradually die off so i can say by combining the two electrons at two states i can say as if i have an electron at that location right otherwise i don't know where the electron is the plane wave probability of finding an electron is same everywhere in the other case so by interfering them i can say where the electron is now what will happen a little bit later a little bit later you see what will happen is because the delta because the e and delta e are slightly apart or this delta e apart so what will happen that a little bit later the red one will move to the right but the blue one will move at a slightly different velocity to the right because it has a slightly different energy slightly different omega and so it moves slightly to the right now the point where they are interfering is not constructively is no longer at x equals zero you can see they are interfering at a slightly downstream constant so as if the original electron which is sitting at x equals zero that as if has moved down to a certain distance and if i could somehow capture this information then i would know what velocity an electron moves if i put it in a certain band at a certain point now in order to stay on the peak what i need to make sure that the right hand side the blue side of this equation that phase does not change with time so that delta kx minus i delta e h bar multiplied by t that that remains a constant because then that will have a constant shape that i can follow i'm sure this step you probably didn't follow this you have to think a little bit that why on the peak and if you plot out some of the way functions very easily you can see it numerically but if this has to be a constant then i can say that the velocity v is delta x over delta t right this is by definition that at a certain time how far it moves delta x over delta t is velocity but you can see from the top from the blue exponent that delta e over delta t is essentially can be given by delta e over h bar divided by delta k do you see this from the blue just do this one step and then you'll see that this relationship emerges and from here you can you can see that the value of a the acceleration the acceleration is simply delta v over delta t which is the Newton's law simply Newton's law take one more derivative and when you take one this derivative and follow this equation through you will see that this actually looks like a Newton's law you can make it look like a Newton's law the this is sort of difficult to go through the equation but it's something i i guess you have to just write it in a page but the bottom line is that you could rewrite it such that that derivative of h h bar k what is h bar k that's the momentum derivative of h bar k with dt so change in the momentum as a function of time what is that that's force so anything that is left anything that's left if i call it en masse if i call it en masse then i can make it look like a look like a Newton's law as if in a like you know that is i have an atom i have an electron and then i apply a force and it keeps moving with a certain effective mass not the original mass you can see on the left hand side there's no definition of mass at all there's no or no notion of a mass at all there's no m not sitting here right so free electron mass but only thing that is sitting here is delta e over delta k that's how the solution changes in each of the band right so let me show you how it works it's better to show it with an example so let's take the any two bands let's say the third and fourth band i'm not showing the first and the second band let's take the third and fourth band let's focus first on the red band now velocity i have told you velocity is given by delta e over delta k divided by h bar that's the velocity if i look at the red curve if i change the k a little bit to the right hand side the energy goes up so therefore my velocity should be going up do you see do you agree with this statement that if you have if you are sitting on the bottom then the solution is symmetric on the left and right it goes through a minima so when you take a derivative the value is zero as you move away from plus in the plus k direction the velocity generally goes up and then eventually it will come down and similarly on the left hand side the solution is symmetric so the velocity would be going negative and then going back to zero does it make sense it should be in some way right because remember with plus k electrons are supposed to go to the right and the velocity should be positive because it's going to the right you can see indeed the velocity is positive because on the right hand side you can see velocity is indeed positive with minus k velocity should be the electron should be going the other way and the velocity should be negative and it is indeed negative you can see right because below the zero axis so that makes sense what about the effective mass the effective mass is a second derivative of energy with respect to k and you can see here if you take the second derivative of that first equation then you will get something like this and you can see that the mass this particular mass actually is not a constant it changes with position because the curvature of the solution changes and therefore this one changes as well but the main point is very close to k equals zero you can see it's approximately a constant and we'll use that information later but throughout the zone or throughout this solution space of course it's not a constant because the solution of the equation is changing throughout and similarly you can figure out that for the holes this should be the opposite the effective mass should be negative in one case and the electrons should be going in the other way so the for the blue bands and implication of this we'll discuss a little bit later now up to this is what is in the book and you are supposed to know all this but the professors are very fond of setting the following problem for the qualifying exam what if you do not have second derivative what do you do generally at that point you see the question and you say okay today the exam is not going to go well for example this particular case on the left hand side I have an energy by the way the x axis is k the wave vector right remember the solution space plus pi over p minus pi over p that's the two boundaries of the solution now instead of a straight line instead of this nicely curved solution I somebody gives me a straight line solution there is a material called graphene that people are very interested in that has some of these features at least in part of the zone it has this some of the solution what do you do now well first thing is that if you try to we'll look at the equation in a second so don't worry about it but first let's try to see velocity first derivative of the energy versus k well that's fine no problem because it is a straight line I can take a derivative and if I take a derivative then on the right hand side plus k I will have a constant velocity on the left hand side with minus k I will have a negative velocity no problem now what are you going to do when you are want to take the effective mass if you try to take a derivative of this what will be the derivative it will be 0 what will be the effective mass infinity right 1 over effective mass is the second derivative second derivative 0 effective mass infinite does it mean you pump and you put an electric field and electrons and want to move actually that's not the case so that very definition of effective mass doesn't hold anymore because we cannot write the Newton's law as we did in that previous case when you have a continuously carving back but the solution is still available because remember what we want to know that as a function of time how the energy how the position and the momentum of the electrons are changing that we already know from the first two equations for example you can see that if I if the force is the derivative of k with respect to time you know change of momentum with respect to time if I knew the force at a given point the electric field let's say coming from the electric field I could just integrate for that time for a certain time delta t and I will know the new k so it's starting with the momentum I know the force so after a certain time delta t I will know what the new momentum is similarly as soon as I know the velocity I could integrate the velocity for a little bit of time and I will know where the electron originally was and where the new electron is right so in fact I do not need effective mass I can solve the whole problem not even needing an effective mass and everything will work or just fine so variation of this problem are often said just to test whether you understand that effective mass is not fundamental it is helpful many time it works it's a historical baggage many modern materials don't have effective mass but not having an effective mass does not mean that electrons do not move easily through the castle in this case in fact electrons moves very easily through graphing you see this point okay so it's a long lecture but let me conclude so we first said the solution of the Schrodinger equation is easy if we have well defined periodicity 80 percent of the material of interest is not periodic but it's easy to solve we'll solve it here and then for many other material amorphous polycrystalline and we'll say well I cannot solve it over there but it's almost like a periodic crystal because most materials are now we said that electrons can sit in narrow energy bands and not necessarily narrow in various energy bands and we showed how to calculate that and these bands are separated by a gap so electrons cannot sit everywhere remember we said all electrons are not equal so therefore different electrons have different band curvature in which they sit in the towards the bottom electrons don't want to move remember they were relatively flat so when you take a series second derivative and when you have the effective mass inversely proportional the electrons in the bottom band they don't want to move these are valence electrons they don't want to go from one one atom to the next as you go up and up and up the curvature becomes larger or curvature becomes larger and the effective mass becomes smaller electrons can move through the crystal easily see and the final point is that the effective mass is not a fundamental concept I just emphasize that and we shall see how to solve k dot p model in real crystals because this was a fake crystal one-dimensional well what what is the last time you saw a one-dimensional crystal in a such a simple form but many of the features of the actual crystal are actually reflective of this variation everybody has bands everybody has this brilliant zone everybody has effective mass if it can be defined so the real crystals in many ways contain many features which are very similar to this k dot p model okay k p model or chronic penny model the people who first solve this problem okay take a look I skipped a few things but take a look in your book and understand this clearly it looks very simple and I am sure some of you have read this information before in undergraduate but to really deeply understand this is very important because most of these concepts we are learning now towards the end of the course you will see and also in other courses that this is a basis most of them don't apply anymore but if you don't know what are the approximations built into the classical theory you will not know when they are breaking and therefore when new theories have to be applied so understand every assumption with the details not just glossing over it right okay thanks


Methods of teaching vocabulary in the classroom. While sentence structure and grammar are the foundation of the English language, vocabulary is the glue that holds it together. An expansive vocabulary allows students to feel confident in their abilities, and communicate more effectively. There are many methods of teaching vocabulary, and in each class the teacher may need to use different methods. This is because each class will be made up of different students each with their own learning style. What is Vocabulary for? Vocabulary is important to teach in the very first lessons, because it is how students will be able to understand the words they need to use for basic communication. Vocabulary is found in every stage of an ESA lesson. In addition, vocabulary can be taught several ways. Pre-teaching and reviewing vocabulary in the study stage, and then using that vocabulary in the activate stage is a good way to scaffold a lesson. However, before vocabulary can be taught, it needs to be properly selected to ensure it is relevant to the lesson and at an appropriate English level. Some of the most effective ways of teaching vocabulary are using visuals and planning engaging activities. Visuals such as pictures can be used to pre-teach vocabulary for the daily lesson, and review vocabulary from previous lessons. Other engaging activities include games and role plays. It is also important that teachers use multiple methods to teach vocabulary, to keep students engaged in the learning process. The more students use the vocabulary, the higher the chance that they will remember it. Therefore incorporating relevant vocabulary in every lesson is crucial. Lesson Structure All lessons should have some focus on vocabulary. Lessons should check to understand previous material. Pre-teach new material, have students practice reading, writing and speaking, using the vocabulary. A sample lesson could entail the following. Sample lesson plan. Engage, students talk about their weekends, focusing on vocabulary learned the week before. Study, teacher pre-teaches vocabulary that builds on previous knowledge, that is relevant to the lessons. Students do a worksheet that requires them to match words with definitions or pictures. Students are given a picture and asked to write a story about what they think is happening. Activate, students are asked to present their story to the class. Depending on students' age. The method of teaching vocabulary also is dependent on what level the class is. The sample lesson above is an example, that would be more suited to intermediate to advanced classes. An advanced class can understand more directions to activities than beginner classes. For beginner classes visuals are more effective than activities, because they require less understanding of English. An example of a more beginner class could entail. Engage, students play a game of Simon Says as a warm up to review the previous vocabulary. Study, pre-teach vocabulary using pictures. Have students do a worksheet of matching vocabulary with pictures. Activate, have students create a drawing labeling all of the vocabulary that was taught. Also teaching vocabulary online versus in a classroom looks different. In a classroom there is more room to interact, while online the teacher is limited by the computer and what can be seen on the screen. This means the teacher has to be creative with visuals. This could include making games out of the visuals to keep it engaging. Do you want to teach English abroad? Take a TEFL course today? Several concepts are certain no matter what level the class is, or how the class is being taught. First, vocabulary must always be relevant and accessible for the student, and second, it must be as engaging as possible. And click on any of the videos here on the left for more interesting teaching tips for getting certified to teach English abroad and online.


Okay folks, well it's up up and away with the green lights flashing in Wall Street once again Dow S&P, Russell all of them are up strong, NASDAQ is up almost 100 points, S&P is up 25 handles making new highs on the day and also we have the Dow Jones which had been down 300 points is now up 80 on the day. So there's a lot of buying coming in Apple, Google, Tesla all of them are up today it looks like and things are back in the green again with the exception of Treasury bonds and Treasury notes they're down just a little bit but other than that the rest of them are pretty much under a great deal of trouble here. Now if you hold on just here one second I have to do something to turn something off because we're just getting an alert here in the Dow Jones and it's making new highs and I wanted to make sure that you folks get a pretty good idea of what's happening with that. The Dow Jones today is going to be Alfie Lavoie of AIR Software he is the grandfather of all this folks he's the one that built the Astro program that Bill Meridian and everybody uses they all built it over a 20-some-year period he'll tell us about that but he is a he is a he's been on TV and so many things I mean he's just he's been around for a very very long time and he's very entertaining super nice guy super super what do you call it humble and he's married to one of those beautiful girls you'll ever meet the moon angel yourself Carol so we're going to have Alfie on at the break here which will be good on Monday we're going to have Mike more of more analytics which we need to have Mike because we've got new highs now in the crude oil market we got up above 37.73 dollars a barrel today we'll be talking about that on the beginning of the show for Fibonacci 24-7 because it is a what we call a classical pattern of what we're watching here you know with some of these things here so it's very very interesting to see how these things unfold here today but the strength in the market is to be expected I guess because it's been very very strong we had that big break that we expected the Dow was down 550 points on Tuesday and then Wednesday and then it comes back on Thursday and Friday and has gained almost all of its all of its losses so that's the main thing that we want to be watching we get back from our break here we're going to be talking about the crude oil market because we think we're at a very critical junction so<PHONE_NUMBER>