Coming up on DTNS, Samsung leaks its announcement during the Oscars and confuses some people. Google goes to court in the EU and why the director of Thor could conceivably force Apple to make better keyboards. This is the Daily Tech News for Monday, January 10th, 2020 in Los Angeles. I'm Tom Merritt. And from Studio Redwood, I'm Sarah Lane. And I'm Roger Chang, the show's producer. Joining us is UK's associate editor at the Mac Observer and author of Not Buying It, the Facts Behind Fake News. Charlotte Henry, welcome back to the show. Hello, hello. Thank you so much for having me. How are you both doing? Ah, we've been doing well. It's good to have you. We have, we have weird Oscar news in the tech news today, one of which you wrote up for Mac Observer that we'll be talking about in a little bit. We were talking full award season. Yes, kind of, kind of with machine learning and keyboards. And Samsung ads. We talked about the Oscars quite a bit in Good Day Internet. If you want to get that expanded discussion, go to patreon.com slash DTNS. Let's start with a few tech things you should know. The Israeli newspaper, Haaretz reports that the Elector app was used by the country's Likud political party and contained the usernames and passwords of all admins in its source code, allowing anyone to log in and download the country's voter registry of 6.4 million eligible voters. The developer of the app confirmed the vulnerability and stated it was a one-off incident that was immediately dealt with. Coronavirus updates. Foxconn received government approval Monday to resume production at its Zhengzhou plant, but its major Shenzhen plant remains closed. They're still waiting for approval to start that one back up. Meanwhile, Sony and Amazon announced they would not attend Mobile World Congress in Barcelona this year over concerns about the epidemic. Cancelations now include those two companies, Samsung, I'm sorry, Sony, Amazon, LG, ZTE, NVIDIA and Ericson. Samsung's still going. Mobile World Congress organizers will also not allow travelers from China's Hubei province to attend the event. And all other Chinese travelers must show proof of being outside China for 14 days before they are allowed to attend Mobile World Congress. Sounds like a fun, logistical thing for organizers of WC. ARM announced two new processors, the Cortex-M55 for embedded devices and the Ethos-U55 micro neural processing unit designed to offer a higher performance machine learning on edge devices. The Ethos-U55 is a co-processor to the Cortex-M line with ARM claiming a performance increase on ML workloads of 480X. And one more tidbit coming out of Uber's earnings report last week. Uber claimed it provided 14 million rides in India in 2019. More than 50 percent of that country's ride-hailing market. Uber plans to expand from 50 to 200 cities served in India by the end of 2020 with the focus on onboarding drivers of two-wheeler and three-wheeler vehicles, which are used quite prevalently there. All right, let's talk a little bit about that Samsung ad. Yeah, the Oscars don't always make it in the show, but they did this year. Samsung aired a commercial during the Oscars showing a previously unannounced foldable device, which we all assume will be called the Galaxy Z Flip shown in purple and also in black. The phone uses a clamshell form factor, but doesn't appear to fold completely flat. It was shown sitting on a table at a 90 degree angle and with a small full color display on the front showing color ID with a slider to accept calls while folded. If you were paying attention and notice at the bottom of the screen stated, you may notice a small crease in the center of the main screen, which is the natural characteristic of the screen. The ad promised more details at Samsung's unpacked event of February 11th, which is tomorrow. I watched this ad and the first thing I thought was, oh, an Apple ad in the Oscars. And then this phone started folding and I thought, wait, is this razor? And then I realized that that didn't look like the Motorola razor. And I waited to discover it was a Samsung ad at the very end, which is interesting, Charlotte, because this is Samsung having an ad for a mainstream audience a day before it actually announces the details of a product. So that's very interesting. And I guess this is kind of an equivalent of doing a Superbowl ad, isn't it? It's a kind of big, big, you know, live as big. But yeah, it's along the same lines. As we said earlier, you know, it was a relatively small audience for Oscars. But, you know, it's a lot of people watching something live. But first of all, I was amazed. It looked like a mirror that I put in my handbag. The little like like a compact. Yeah, exactly. I have to be honest, I don't get the foldable phone thing. Like, didn't we do that in the early 2000s? Haven't we done that?  Doctor, doctor. Side effects may include a crease screen so that when you're. That means it's working. And, you know, and they've all and they've all kind of lot of the companies have been trying to push these products and the kind of we know there's been a number of issues, though, creating these foldable phones. And I just can't see what advantage, what problem they are trying to solve by creating these products. Yeah, I'm still hung up on the idea that you and maybe this this this is why maybe they know people aren't clear on what a foldable should do. So seeing it in action ahead of the announcement might make people more excited for the announcement. That could be the thinking or it may be just that Samsung realizes like we none of us can actually keep all of these details from leaking anymore. So we might as well lean into it and just put an ad out there. I have to say, though, if I'm watching the Oscars as an average user, not a DTNS host or even a DTNS listener, probably, I'm probably like, oh, I'm going to go into the Apple store tomorrow and get that full foldable phone because it really looked like an Apple ad. And nobody understands Galaxy unpacked what that is. Like they if if anything, they might know it was Samsung that did it. But it could be very confusing for people. It didn't look very Apple. It's funny, though. There was an Apple commercial that was about like Night Mode and it was a smashing pumpkin song. And I felt the same way. I was like, this has to be an Apple ad. But are they going to surprise me to be another company? Like we're getting to the point now where we're like, oh, this is a well, well done ad. Who is it? Adobe added ad and it was very clearly Adobe from the beginning. So I commend them for that. US Senator Josh Hawley published a plan to remake the Federal Trade Commission to provide more direct congressional oversight as well as better scrutinization of big tech, calling out Google and Facebook by name in the proposal as instances of the Federal Trade Commission failing to protect consumers. The plan would put the FTC within the US Department of Justice and replace a five commissioner panel, which is what it has now, with a single director confirmed by the Senate. The existing panel is also confirmed by the Senate. But the commissioner of the panel gets chosen by the president out of the panelists. This would say the president would appoint a director and the Senate would confirm them and then they'd run the FTC. That's it. It would also create something called a digital market research section to specifically look into issues around technology. Holly also called for new legislation to give the FTC the power to levy fines on first time civil penalties. Right now, the FTC can't do that. And that's why Facebook didn't get fined for the Cambridge Analytica data misuse. Would give the FTC authority to enforce data portability and interoperability standards and give US state attorneys general the authority to enforce the same laws as the FTC. So you wouldn't have to wait for the FTC to enforce something. Yeah, I mean, my first reaction to this is, OK, well, how much power does Senator Josh Hawley have? How far is this going to get? And if it would pass as law and the FTC was reworked, is that a good thing? You got a lot of people who are going to say, no, not too much. Government control, that's frightening. But we're also in a bit of a mess with some of the companies that are being called out here. So what's the better strategy to keep things the way they are or to change things as you've just laid out? I confess that the senator in question is not a household name in the UK. But what I think is interesting is more and more lawmakers in different countries in different institutions are all taking swings at big companies now. We're going to see that in the next story we discuss as well about Google and the EU. But, you know, across the board, this is happening now. And I think in a way, the tech companies have bought this on themselves. They've felt almost unregulated, unregulated for so long. And they've almost I think politicians have felt that they couldn't regulate them. And now there's a lot of pushback. It's a vote pleaser.  I'm concerned about the idea of writing, changing a government agency like this specifically for the purpose of going after big tech rather than trying to improve it so that it just works better in general, because once big tech stops being the problem, then it may not work very well for something else. So I'm not a huge fan of just rewriting it for the purpose of the moment here. But you mentioned that EU story. Sarah, tell us about that. Yeah, Wednesday, the EU General Court in Luxembourg will start a three-day hearing of an appeal by Google to overturn a 2.4 billion euro penalty for abusing its search dominance to the disadvantage of smaller shopping search services. Google argues that services did not appear high up because they weren't good enough, not that Google demoted them. Regulators found that Google prompted its own services at the expense of competitors, though. The judge's decision may not arrive until next year and appeals could last longer until it has a case which still isn't resolved after more than a decade, 10 years. They're still working on that. The EU also levied fines for linking apps to Android and abusing dominance to the disadvantage of advertising rivals. Yes, so there's a lot going on here. And what's interesting is that, as I said earlier about US lawmakers, the EU is really taking a swing at this. This has been an ongoing issue for a bit. There's been a new commission, which is the executive body of the EU has come in recently. They've been really going for this. It's been going on for a number of years now with the competition commissioners who are there. They're really determined to make a stand on this. And it tends to come through Ireland, which is obviously an EU member and where a lot of US tech companies have their European headquarters. So if you see data protection issues that happen in Europe, it often happens through Ireland. And so Google is just one of the companies facing trouble here in the EU. And yeah, as you can see, these things do take a long time to shake out in the EU. There's a lot of hoops to jump through, but they're not letting go of this. Things like Apple was told, there's been talk of having universal charges in Europe. That's all coming through the EU, really pushing back and trying to make a stand at big tech in the way you were describing American politicians are doing as well. And because obviously it's a multi-country block, it does have some authority to take, to fix it across a continent almost. Yeah. Margaret Bestiger, in particular, now in charge of that competition commission that you're talking about, has in previous roles been fighting against these companies and probably to their sadness, she's not going away anytime soon. No, she's not. She's in the team. She has been very, very prominent on this issue, as you say, for a number of years. Yeah. So again, that is a three-day court hearing that will take a year to have a decision, which could then be appealed. So it's not like you're going to expect Google to get finalized, but these things do have effects on companies and companies will often change their behavior in the meantime to make themselves look like better citizens, such as with Android changing how it bundles in apps related to a different case in the European Union. But it can have some sort of ancillary effects in that way, even if it's not resolved. Yeah. And I may be getting my EU law institutions wrong, but I'm pretty sure the general court is not the highest court in the EU. No, I think you're right. I may be getting a wrong shoe, but I think you're right. It's not specific. It's in neither of our countries a part of the EU anymore, so. Oh, that's right. Yeah, that's weird. All right, the group behind the big ML machine learning platform used some deep neural networks trained on factors that were considered predictors of an Oscar winner. The idea was, let's see if it can see the patterns in what won before and then make good predictions about what will win this year. The algorithm used things like film synopsis, other award show nominations, film festival prizes, and the like to get trained. And of the eight categories it made predictions for, it got five right. I did better on my ballot, I'm just saying. It went against Oddsmaker's Choice 1917 and predicted once upon a time in Hollywood would win Best Picture, but neither were right because Parasite won. The algorithm also predicted the Irishman would win Best Adapted Screenplay. The Oddsmaker's favorite Jojo Rabbit and the Oddsmaker's won that one. The algorithm also got Best Director wrong. So the bookies did better than the algorithm. And I think this is a great example of the limitations of machine learning. They trained it on some stuff that showed what the patterns in the past had been, but it wasn't the right stuff because past patterns don't always hold in current conditions. There's, oh, go ahead, Charlotte. No, I was just gonna say they really don't when human beings are ultimately making the decision. It turns out we're kind of fickle and sometimes unpredictable, right? I think they can get this to be better. I think we're somewhat predictable, although you're right. We do things that are unexpected, but you've got to have the right information. And that information may be like, how to predict the, when does fickleness play in? I don't know how you quantify that. This is not a kind of Nate Silver baseball spreadsheet where you have so much available data that it's useful to an algorithm. It seems to me this is too limited to dataset. It also kind of assumes that, oh, if certain kinds of art were made in the past, then the same kinds of art will be made in the future. And I mean, that's just the antithesis of the whole idea of art. There are definitely some metrics here where it's like, okay, well, you're getting close to the way that the Academy has voted in the past, the type of movie it is, who's involved in the movie, who the director is, and that kind of stuff. But there have been so many surprises. And I mean, I get my Oscar poll, I'd never win an Oscar poll. I'm always wrong on lots of things, but I feel like I also take a lot of time to watch stuff and I'm surprised all the time. So a machine isn't gonna be able to be better than that. I think it could be. But I think the- Could be, sure. What we're seeing here, another thing we're seeing an example of is bias in datasets. And I think you nailed it, Charlotte, it's the data. You have to have the right data to make this predictive. And it may be that I'm wrong because there may not be the right data out there, but they certainly haven't found it for this particular problem if it is out there. The US Justice Department charged four officers of the Chinese People's Liberation Army by name with crimes related to the 2017 Equifax data breach. The indictment includes three counts of conspiracy to commit computer fraud, conspiracy to commit economic espionage, conspiracy to commit wire fraud, and a charge of economic espionage, three counts of wire fraud, and two counts of unauthorized access and intentional damage to a protected computer. The indictment claims that the defendants gained access to Equifax's system through an unpatched Apache Struts vulnerability about May 13th around that time, running more than 9,000 queries over the course of two months to obtain trade secrets along with personal data on nearly half of all people in the US, as well as a million UK and Canadian citizens. The intruders were allegedly, the intruders allegedly cleared logs daily and used encrypted communication within Equifax's systems and then routed traffic through dozens of servers across 20 countries to cover their tracks. Yeah, there's not much else to say here other than this is a message. We're certainly not gonna see these four officers come to the United States to stand trial. They're gonna stay in China. China will certainly, and they may have already by now denied the charges. But this is the US trying to say, if you come into our systems and attack us, we will be able to figure out who you are. I think this is interesting in the context of what we're having in the UK as well, where we've had a big debate over the use of Huawei in building our 5G infrastructure. And the Americans, the American administration, as you know, has been pushing back very strongly in telling the UK not to allow Huawei any involvement. And it is because of incidents like this, right? And it's, as you say, this is the Americans take trying to make a stand against the corporate national espionage that we all just kind of assume, let's be honest, happens from the Chinese state, and which is why companies like Huawei are feared. And so, you know, there's clearly a move happening at the moment where Western states, the US, led by the US, are trying to push back against this kind of digital corporate espionage that is obviously concerning them greatly. And let's be honest, you can understand why. Yeah, and I'll be honest, the idea of officers in a foreign army being charged with breaking into something like Equifax and accessing information concerns me way more than the potential possibility that there might be an undetected backdoor in a piece of Huawei equipment. I'm not saying that either are zero risk, but one is a much higher and more likely risk than the other. So I look at this stuff and I'm like, if I'm China, this is the kind of thing I do. I go after Equifax and hope I don't get caught. In this case, the US seems to have uncovered who was responsible.  It's huge, yeah. Because we've had so many of these different kind of major incidents and we have, but that Equifax story really was a kind of moment in time when you've suddenly got 145 million US citizens having their data stolen. And we kind of, from the Chinese by the Chinese, that is a huge moment. And I think we would all do well to kind of remember that sometimes because in the tech world, we move on so quickly from things. And that really was, like I say, a moment in time, wasn't it? I remember where I was when I read the story. I was in physical therapy getting my shoulder worked on and waiting for an appointment. I was reading it on my phone. Hey, folks, if you want to get all the tech headlines each day in about five minutes, be sure to subscribe to DailyTechHeadlines.com. In an Oscar press conference, winner for the Oscar for Best Adapted Screenplay for JoJo Rabbit, Taika Waititi, was asked what writers should be asking for in upcoming guild discussions regarding a new labor contract. There's the WGA, which is the Union for Writers, is renegotiating its labor contract with directors. Waititi didn't answer that. Instead he called on the WGA to get Apple to fix its keyboards. Here's this quote. Apple needs to fix those keyboards they are impossible to ride on. They've gotten worse. It makes me want to go back to PCs because PC keyboards, the bounce back for your fingers is way better. Hands up, who still uses a PC? Like he literally called for the press to tell him, which of you use a PC? And then when someone raised their hand, he said, you know what I'm talking about. It's a way better keyboard. Those Apple keyboards are horrendous. He also expressed a preference for deeper travel in the keys and complained of inflammation in his shoulders and tendons and related to the narrowness of the keys. I'm assuming he's not talking about the 16 inch MacBook Pro that came out last fall, but the years of Apple keyboards about which everyone has complained, right, Charlotte? We now cut to our special butterfly keyboard correspondent Joanna Stern at the Wall Street Journal. Do you remember her piece? Oh, gosh, yeah, yeah. No, absolutely. So, I mean, I assume that's what he was talking about, right? He has to be. The butterfly keyboard, which has been horrible for years. The 16 inch is so much better. I can't believe that he wouldn't have at least toned down. The old butterfly keyboards that have been out for several years now, I mean, there are a couple of people I've met who like them, but most people do not. So I was on air earlier with one of them. John Martellaro, who's a wonderful writer at the Mac Observer. He told me I was wrong about the butterfly keyboard and he really likes his. He is the only person I've ever found that likes it and hasn't had a problem with it. Like I say, that famous Joanna Stern article where she kind of highlighted all the letters that didn't work for her and loads of people had had the same problems. I mean, I do find this story kind of funny that he was like, I'm at the Oscars. I've got one of the biggest awards of my life. Yeah, I'm a writer, darn it. What am I going to talk about tonight? I'm going to talk about Apple keyboards. He doesn't want to answer the sensitive WGA question. I get that. The fact that he picks Apple keyboards to pivot his answer into is hilarious, which is Taika Waititi. He's hilarious. But also I felt like it was real. Like he really is railing against this. And I'm sure Apple won't respond to this in any way. If they were to respond, I'd say ship him a 16-inch MacBook Pro and see if he likes the new keyboard. And I'm sure they will. If I could just be the dissenter, just for the course of discussion. I don't hate my MacBook keyboards and it's the same keyboard that he does not like. I just don't hate it. Maybe I just get used to things easily. I've also had a lot of RSI trouble over the last couple of years, so there's that. But I just don't, I don't know. I don't know what people hate so much about it. Is it just, what is so hateable about it?  I just don't feel like I'm pressing the buttons. Huh, I just, I don't quite get, I don't get the hate. I feel like he's like, it's impossible to type on. I'm like, well, no it isn't.  That's not impossible. No, but he's exaggerating. Maybe I have gotten conditioned to something that is really bad for me. It was a revelation when I got back to town. I think he was possibly pushing his luck when he was trying to claim that the butterfly keyboard had given him RSI. But I do think probably that I'm using quite an old keyboard here. I don't, I don't think this is one of the butterfly ones. I think I'm pre-butterfly. Yeah, yeah. But, you know, I can see, like you do want a bit of sturdiness in your keyboard.  But one, get a better chair. Two, he's kind of right. Like the butterfly keyboard does suck for most people and Apple has been really embarrassed by it. And actually, the fact that this happened at the Oscars and has got so much pickup, I actually think he's really embarrassing for Apple. It shows that there's real frustration out there. I'm in Sarah's position on the Apple TV remote. I don't mind it at all. I think it works great. Everyone else hates it and Apple should change. But you don't know which way around it's meant to go. Yeah, you just feel for the menu button. Yeah, I did, but no, it's not good enough. But it's the same argument, right? It's the argument, it's just like, it doesn't matter that I like it. Most people go. It is a good comparison. Yeah, once you say Apple TV remote, I'm like, it's the bane of my existence. Look, Sarah doesn't have type of feelings about the MacBook Pro keyboards. Sarah is legitimately angry about the Apple TV remote. I know, I shouldn't have brought it up, I apologize. Not good enough. Come on, it's a Monday, don't, I know. Hard enough. But when you, I guess my point is, when you have this much opinion about something, it's not just a bunch of people jumping on the bandwagon. I think there's something real behind it. And having a major director and writer call it out and having, not just having him call it out, but it wasn't dismissed as like, well, that was weird. It was people going, yeah, no, I'm with him on that. Well, and it's a complaint that we're all familiar with. Yeah.  It's like, oh yeah, this guy too. Everybody hates him. It would be, so Apple obviously hasn't commented. I wonder if the writers Guild of America is gonna say, like, is it gonna actually have to dignify this by saying, no, we're not getting involved in a dispute with Apple. You can write however you like. Yeah, it's okay. We'll keep track of that. This is best for you. The other thing I like about this story is that a PC is like the ultimate insult. It's so bad I'm going back to PC. Yeah, he did throw a PC under the bus a little bit, backhanded compliment there.  A Microsoft should send him a Surface Pro and Adobe software installed on it. That's the PR crew right there. Right, right, right.  Yeah, yeah. Keyboard stories sometimes hit our subreddit. If you care about a certain story and you want to vote on others and let us know what you care about us talking about, dailytechnewshow.reddit.com is our subreddit. Please join in on the fun. Speaking of fun, also join our conversation in Discord, which you can join by linking to a Patreon account at patreon.com slash dtns. All right, let's check in with Chris Christensen, the amateur traveler who has a product tip for those of us who want a little more security from our luggage. It's Chris Christensen from amateur traveler with another tech in travel minute. I just got off an interview for an upcoming amateur traveler show about Ecuador and one of the things my guest mentioned was a friend who had their bag slashed and their iPhone stolen while they were on a bus. And that reminds me that we haven't talked about on this segment, products from Pacsafe. And Pacsafe is a company that has backpacks and purses and things like that that are theft resistant. They have mesh embedded in the fabric so that they're slash resistant. And we actually use those, my wife and I, on our trips and find them just a little more piece of mine against theft. So check out pacsafe.com. I'm Chris Christensen from amateur traveler. Indeed, and certain places you go, that's an important consideration. So thanks for the tip, Chris. Let's check out the mail bag. Let's do it, Rob from recently Stormy London writes in about our conversation last week about somebody who had bought a used Tesla not getting the package that they thought that they were paying for. Rob says, Tesla software-based upgrade packages seem to be a strange mix of physical items which can be resolved and game our software license keys and are usually bound to an account on first use. The question in my head is this, when purchased, is the upgrade tied to the item or to the user? Since the upgrade was removed for the second hand buyer, it would indicate the latter. That being so, if somebody buys the autopilot upgrade package on their first Tesla, could they apply that upgrade for no additional fee to their second Tesla given their purchase history? These are great questions, Rob. As far as we know, I have not seen any evidence that Tesla lets you know your purchase is tied to the user. Tesla may come forward and point out somewhere that I haven't seen that that's the case, but I haven't seen that yet. Nor do they give you the option to take your autopilot upgrade package along to a different model. I imagine that might be negotiated if you traded it in or something, I don't know. But you are asking the right questions, which is you need to know up front what the rules are. And I think that's what caused so much frustration with this guy who bought a used, because he said, look, the invoice, all the paperwork said it was there and then you took it away. Like if you had said from the beginning, like no, this doesn't go with the car, that's one thing. This seems to be more broadly a kind of Tesla trait, doesn't it? It's not the most transparent company in the world whenever I look into it. Whether it's been through prices where we keep getting told the prices are coming down, the prices are coming down and they still stay pretty high. They never get to, these type of, I think it makes consumers who maybe wanna move to an electric vehicle, who wanna make some changes. I think it makes it more difficult for people. And I mean, the example of upgrade packages and buying it secondhand is a really good example of something where a lack of transparency would put you off buying a product. Oh, and by the way, it's still Stormy London. I nearly got blown down the street this morning. We got some of your wind over here. It's been really windy in a way. Excuse me, it was a rough dinner. Oh, I'm sorry. Hey, shout out to patrons at our master and grandmaster levels, whether it's windy in your area or not, including Chris Smith, Jeff Wilkes and Sonya Vining. Also, thanks to Charlotte Henry. I hope you're staying safe in the windy and stormy London area of your part of the world. Let folks know where they can keep up with the rest of your work. Okay, so yeah, come join us over at themacobserver.com. I'm obviously on the Twitters at Charlotte A. Henry. And yeah, and there's obviously a link to my book on the Amazons in my Twitter bio. So come check that out as well. Absolutely. Also, folks, don't forget we have new Patreon reward merchandise celebrating six years of DTNS. Len Peralta created a six year anniversary logo for us. And if you back us at certain levels at patreon.com.slashdtns for three months in a row, you get either a sticker, a poster, a mug, or a t-shirt with that logo on it. Go check out the details, patreon.com.slashdtns.slashmerch. Six years. I know. Thank you. I know. Hi. How about that? If you have feedback for us, if you've been watching the show for six years, listening or any portion of that, feedback at dailytechnewshow.com is where to send those emails. If you'd like to join us live, we'd love to have you. We're live Monday through Friday at 4.30 p.m. Eastern 2130 UTC. And you can find out more at dailytechnewshow.com.slashlive. Back tomorrow with Patrick Beja. Talk to you then. This show is part of the Frog Pants Network. Get more at frogpants.com. Well, I hope you have enjoyed this program.


My internship is research-based, so most of the work is trying to prepare a research report that's going to be useful for my MP. She's the Shadow Secretary for Defence, so she's interested in the issue of peacekeeping and Australia's involvement in peacekeeping in the region. And I'm doing international relations, so peacekeeping is the last part of Australia's international relations with the region. So I think my knowledge has definitely been very useful towards my internship. It's been a fantastic experience, so I get really involved in what's going on in the day-to-day life of parliament, including city weeks and senate committees. It provides an excellent way to use your academic knowledge in a policy setting, especially because the politicians will actually use your reports for practical policy purposes. It's definitely given me an insight into where I might want to go in the future, and it's given me a whole different experience than what I would have expected. Giving someone an opportunity to work in that environment, perhaps give them some insights and some assistance, provide them with some guidance if that's at all possible, but also mentor them if we can, that to me is what it's all about. Perhaps the star graduate from this program has got to be Michael Kiernan, the current Minister for Justice. So to see people take advantage of what's available in having the experience of coming into the parliament, being in members' offices and senators' offices, and going into various institutions and embassies gives them a much broader exposure to what public life is about. And if we want those people to come back and operate in public service or in public life generally, I think this sort of experience is very good. Well, you just don't get this opportunity anywhere else. The ANU is really where you go to be able to work in parliament and get experience of being here and enjoying the culture of Canberra. Just have a go, just have a go, because you'll be surprised how beneficial it is, how good the experience is. You might meet some grumpy buggers, but that's okay. That's all part of life.


Okay, so we're standing on the severe fault right now this side over here is Basalt you see the dark black color over here again is the eocene pink member of the clarion formation and it's the red Red rock so right now. I'm gonna show you exactly what was going on here What a normal fault means So let me figure this out Richard how do you think I should do this this one's deposited in the lake Later the lava flows came out and they were deposited on top in a cross in various places And then after that the fault broke and this one has dropped down So now that it's next to it rather than being on top of it something like that All right This rock right here is 40 million years old. This is from the eocene clarion formation And it's a lake deposit. This is what we saw earlier and This right here is a piece of the basalt which is my scene which is 10 million years ago and what this would look like in a In cross-section something like This the clarion some more rocks and then the the basalt was deposited on top of it now on the fault on the fault occurred these rocks would drop down along it like that and Now they're sitting right next to the clarion formation which They really didn't have any association before Right now we're on this basalt here On the basalt side and if you can look in the distance there You can see how this this line of this this fault moves right right along into the distance So again the red rocks on that side and the basalt on that side The soil probably It will erode faster and it's probably more More minerals than nutrients in it. Yeah, then just take it then just take a pan from this


For the first time in six seasons, the BSU men's hockey team posted a winning record last year. However, the team made an early exit from the WCHA tournament, losing to Bowling Green in the first round. Now the Beavers are back and feeling like they have something to prove. BSU finished last season one game over 500 with a 17-16-6 record. But this season the Beavers were still picked to finish sixth in the WCHA. Obviously you want to be picked higher, that's for sure. Don't have a lot of respect from everyone else, I guess you could say, but we need to gain that respect. Despite the feeling of everyone outside the program, head coach Tom Saratori and the team have nothing but confidence in their group. I like our team a lot right now and I think probably a lot of teams do, but I like the ingredients that we have. We have the talent and we work hard, we work hard in the gym, we work hard on the ice and I think it all translates to the game. The Beavers return 22 players from last year's team, which has everyone on this year's team dreaming big. We like our team, again we think that we have the ability of winning a lot of games. Right now our expectations are win the league, win the conference and keep rolling from there and ultimately win the championship. And while there are still some questions within the Beavers' decor. We're still relatively young right there with six freshmen and sophomores, but I really like where our guys are at right now. We might be a little young, we might be a little inexperienced on the back line, but we're farther along than I thought we would be a month ago, that's for sure. With 16 forwards and four experienced goalies, the team is going to rely on their offense and play between the pipes to get them through the season. The forward group is strong coming back. We have good teams, speed up front, we have a good skill level. I think we have two to three lines that can score. As far as our goal tending goes, we're very experienced in that position. We're great in the nets, we've got four capable goalies. Any one of those guys could start in any program, so I feel pretty confident in our team going forward. If you've enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland Public Television.


There are the four summarized rules for the quantization, a semi-classful quantization of one dimensional system. The rule itself is very simple, although we went through some pain to get it involving area functions and asymptotic forms, and so on, but the basic rule is really simple, and it has a simple interpretation also. It's said that the area of the ornamented space space, which is otherwise loop-in or PDX, is an integer plus a half times 2 by h bar. 2 by h bar is the same thing as Planck's original constant h. So you can think of the area of one cell, so-called Planck's cells being in the area of h and space space. I'll remind you of the origin of this. Well, let's see. This is sketched in the order of some phase space for a typical oscillator. There'll be things that look like this, and the quantized ornaments are the ones that have an area of 3 plus a half blood cells. So the middle one, the center one, has an area of a half, and then after that, it goes 3 halfs, 5 halfs, and so on. So the area of each little angular region that connects one quantized orbit to the next has an area of one blood cell. Now, I'll remind you that the origin of this formula is that it's a basic idea that as a particle moves around its orbit, it accumulates a phase, which is integral of PDX divided by h bar. This is a very old idea and actually precedes even in a modern quantum. This goes back to the days of the old quantum theory. In any case, you can imagine it's racing out of waves as it goes around its orbit. Now, in addition to that, it loses a phase of minus pi over 2 every time it passes through a turning point. And since we have two turning points in a typical oscillator, that's a total lost phase. And the answer then has to be a integer multiple of 2 pi in order to get phase coherence. I'm repeating some things I said in a previous lecture. So this has to be an equal to 2 in pi. And this condition in this form is the same as the condition of above. It's just rewritten in slightly different language. Here, this has to be a loop in the loop if you're going to go all the way around the orbit. All right. Now, that's the basics of the rule. So I wanted to begin today by making a simple illustration of how we can apply this rule. Let's work with the ordinary harmonic oscillator by zoning this p squared over 2m plus m of omega squared over 2x squared, as I guess you know. The first thing about this classically, we set h equals e. We get an orbit of energy e. And if we plot this in phase space x and p, the equation is that of an ellipse in phase space. So it looks something like this. And if you use, of course, number 12 rule, we're going to need the area of the orbit. Well, the area of an ellipse is pi times the semi-major axis times the semi-minor axis. So let's call this x max here as the maximum position for x. That's the x intercept of the orbit. We get that by setting momentum p equals to 0. So the kinetic energy term goes away and then solving for x. And if you do this, you find that you get twice the energy e divided by m of omega squared. Likewise, let's call this p max here, which is the maximum value of momentum. That's the momentum intercept. We get that by setting x equal to 0 and then solving for p. So that becomes equal to the square root of 2 and e, like this. And thus, the area is, you can calculate the area without doing any integrals. You can get a formula for an ellipse of pi times the semi-major axis, which is the square root of 2 pi, excuse me, 2 and e, times the semi-minor axis, which is the square root of 2 e divided by m of omega squared. Well, maybe I've got the semi-major and minor axis. We've got these reversed, but it won't matter. This is just a product of the two. And we multiply this out. You can see the masses will cancel. And what you get is a 2 pi times the energy e divided by the frequency. Now, like for a summer cell, that has to be equal to n plus a half times a 2 pi h bar on the quantized ordinance. And you can see that we cancel the 2 pi's here and then solve for the energy. And the result is that the energy is equal to n plus a half times h bar omega, which you recognize as the exact answer. So not much trouble for the harmonic oscillation to get the exact answer for summer cell quantization because of the exact initialize. WKB theory does not give the exact wave functions for the harmonic oscillation. It does give the exact energy problem. All right. Now, I'm going to run through a series of examples just because it's so easy to do them and we might as well have some fun just getting some answers. We'll start with some answers so you know when the harmonic oscillator. Let me next do a particle in a box. So here's the axis. Let's say x equals l is the size of the box. The potential energy is that it's zero inside the box but it's infinity outside. So these are hard walls. And the size of the box is gone. Of course, the classical part of the response is back and forth in the box like this. To get the organs in the face space we need to think about face space. So let's plot x and p. Here's the line x equals l again. And the particle is free inside the box. Let's say it has a momentum of p zero just to distinguish the momentum of the particle from the variable momentum p there. So the orbit going across on the right side is a straight line with a constant velocity at momentum p zero. When it gets to the opposite wall it bounces back which just means it changes the sign of momentum. So it changes the minus p pinot and goes back this way with a momentum of minus p pinot. Unless the orbit in face space is really kind of a rectangle and it continues to jump from here to there because it's a hard wall. But I'll fill it in like this if it continues to move back up. And you can see that the momentum is a rectangle in the face space. Now here's a tricky part about the particle in the box. And that is that instead of having a phase shift of pi over two at a turning point we have a phase shift of pi. And the reason is that this is a hard wall. Remember where this pi over two came from? It came from taking the potential energy which we look like this and we had the actual energy and then we looked at the wave function in the neighborhood of the turning point. This is what you call a soft wall where the particle its velocity decreases in a continuous manner. And it was some complicated analysis to get this pi over two but once you get it it's a simple rule. In the case of a hard wall you can see that because the boundary conditions are that the wave function has to vanish at the wall and so you minus five means the reflected wave is minus the incident wave. That's needed to make the sum of the two waves be equal to zero at the wall. So here the Borsomical condition is going to be the area instead of being n plus a half it's going to be n plus one times two pi h one. So it's slightly modified in the Borsomical condition. Now as far as the area is concerned however this is quite easy because it's just the area of a rectangle the height is twice p zero and the width is L so this is equal to two p zero times L. However p zero is just the momentum of the particle so that's the square root of two m e using energy and so I put this in and I'll get two times L times the square root of two m e which is n plus one now times two pi h one and so we'll cancel two's here and maybe I'll leave it in the form of p zero from the time being if I do that what we get is that p zero is equal to n plus one times pi h one and then we get the energy e which is p zero square root of two m which is divided by L p zero square root of two m n plus one squared pi squared h bar squared over two m L squared which you recognize as being the correct formula for the energy levels of the particle in the box here again it goes zero one two three so n plus one goes one two three four the ground state is n equals one now not n equals zero alright so that's another simple example now of course I can help this up for example yes I'm sorry I just gave a solution of why we have n plus one half when we calculate the quantization for the area for the square well versus I'm sorry n plus one through the square well versus n plus one half it's because the one half comes from this the n plus one half that applied to the harmonic oscillator came from the fact there's a phase shift of minus pi over two when you go through a turning point and that's why you multiply it times two so it's half of the phase cycle of two pi that's where the one half comes from up here but on a hard wall you're going to phase shift the pi at each wall because the reflective wave and the instant wave have to cancel out oh okay so that's a hard wall gives you a different phase shift and that's why it doubles the amount of phase and it becomes n plus one alright now I'll do another example this will be what is it going to be this will be the rigid rotor so rigid rotor let's do it classically first the rigid rotor has two masses and m1 and m2 they don't have to be the same this is actually a model of a diatonic molecule which we'll come back to in a few weeks I'd say there's the center of mass right there so I can put an origin and a coordinate system here x and y the center of mass and that's introducing as an angle to the center of mass now this is all classical to the time being the moment of inertia is equal to the reduced mass mu times capital R squared where R is the length of the rigid rotor and mu is the reduced mass so it's 1 over mu is equal to 1 over m1 plus 1 over m2 like that now the classical Lagrangian potential energy but for a rigid rotor this is a free rotor there is no potential energy so it's just the kinetic energy and as you know the kinetic energy of a rotor is one half of the moment of inertia times the the derivative of the angle they make frequency squared which all frequency is 5 dot here it's the rate of rotation it's obviously just constant it's just turning around and around let's translate this into Hamiltonian first of all we'll find the momentum which is let's say we'll call it p5 because it's contrary to the angle 5 this is dL d phi dot and that becomes equal to i times phi dot which you easily see by differentiating i times phi dot however is the same thing as the angular momentum of the rotor well now we have a problem because the angular momentum L is not to be confused with Lagrangian L so let me call the angular momentum Lz just to distinguish it but also if we think about the z axis coming out of the board it really is the z component of angular momentum of the thing rotating alright and then the Hamiltonian is equal to so p5 is the same thing the momentum as we say conjugate to phi is the same thing as the z component of angular momentum but the classical Hamiltonian is p5 times phi dot minus Lagrangian and if you work this out you want to express it that Lz is not in phi but in terms of phi dot so you get Lz squared right about twice the momentum of inertia so I'll write this again in the box because this is the classical Hamiltonian now what about the quantum mechanics of the rigid rotor here we're going to use a process of quantization this is really ad hoc and kind of hand way it's just following intuition but it works like this the process of quantization is that of going from a classical Hamiltonian to a quantum one the quantization that we've used so far in these recent lectures has been called what is called direct quantization I didn't use that terminology but this is what it amounts to in direct quantization what you do is you take the x's and p's which are the classical variables and you've got a classical Hamiltonian h of x and p and you reintermit x as an operator which is multiplication by x on a wave function side of x and you reintermit p as a minus i h bar d x as an operator acting out of side of x so the wave function lives on the configuration space x and this is transcription of classical variables into quantum operators and then the Hamiltonian comes into the operator and this is called the direct quantization of the direct rules for quantization and what it takes you it doesn't take you to the pet space it takes you to the space of wave functions on the configuration space now without a question whether it's valid or not let's just do direct quantization in these other coordinates now the angular coordinates the angular coordinates phi and the conjugate momentum p phi so let's apply this for the case of the rigid rotor in the case of the rigid rotor this suggests that phi, the classical phi goes over into a multiplication by phi it suggests that the wave function is going to be some wave function defined on the configuration space which is the phi angle space and it suggests that p phi which is the same thing as lz should go over into a minus i h bar d d phi and thus the quantum Hamiltonian is obtained by replacing lz by minus i h bar d d phi and hence the Schrodinger equation should be this minus h bar squared divided by twice the momentum inertia d squared psi d phi squared is equal to e psi phi this is the Schrodinger equation based on direct quantization this is easy to solve and you find that the psi of phi is equal to e to the phi m phi where m is an integer and you can normalize it again and m is equal to the integer positive or negative so it's 0 plus or minus 1 plus or minus 2 and so on like that alright configuration space here is we're going to plot this here for phi here's the wave function side the configuration space only goes out to 2 pi like this and the wave functions are e to the i and phi because they have to be the wave function whatever it is it has to be periodic because 2 pi is the same as s5 physically the rotor returns to its original configuration so wave functions have to be periodic and this is the solution we get by solving Schrodinger equation that's why you have to e to the i to the phi periodic functions that's why you get a given integer because it has to be an integer to make this periodic so this is a different set of boundary conditions than we had at the particle in the box instead of hard walls these are but notice that now there's no turning points the angle just increases and phi keeps on going around increasing and increasing so before a summer cloud condition is going to change again because now we won't have any one half at all we'll just be integer multiple to 2 pi well to go through the details of that let's go back to the classical mechanics which we have to do to apply one summer cloud and let's talk about the phase space for the for the system so the phase space is going to be phi coordinate here and the p phi which is the same thing as an LZ coordinate here and we've got 2 pi the periodic and the angle of the pi like this in period 2 pi and what is the classical motion classical motion is obviously one where just phi dot is constant it just rotates in a constant velocity and it will look like LZ is constant so that means the classical orbit is going to just go straight across like this at some given value of LZ which is the constant LZ for the for the motion unlike the particle of the box it doesn't reflect and come back it just keeps on going this line is the same as this line if you like the phase space it's really similar it just goes around and around and around alright so the classical motion has to be this it has to be the area which is going to be the loop integral of p phi d phi must be equal to an integer which I'll call m instead of n now times 2 pi h bar with no one half let me write this way it's m plus 0 m besides that with no one half because there's no turning points on the other hand this integral is just equal to 2 pi times LZ and so look what you get you get LZ to 2 pi is cancelled it's equal to mh bar which is the correct quantization of the z component of any momentum for the energy you get LZ to use the classical formula LZ squared over 2i which becomes m squared x bar squared divided by twice the moment in inertia and these are the energy levels for the the correct answer the quantized orbits are orbits that go across here for m equals 0 it's right on the the phi line they just call it the one like this and the area between them is a single quant cell right so that's the ridge of river there's an example of the book which I think I'm going to skip but I'll let you read it in the book this is the bouncing ball that Zachariah talks about and so this is the idea you drop the ball and it just bounces up and down so it's a particle in the gravitational field except it looks like this I plot the potential energy let's say the potential energy V of x is equal to the energy axis for a gravitational field so this is the potential energy and so the current potential energy is a straight line like this except if it's a balancing ball and we put a hard wall at x equals 0 and then for some energy you like the particle bounces back and forth in this turning point in that one here you've got one hard turning point for the phase shift from the pi and a soft one in the phase shift from the pi over 2 so now you've got an n plus 3 quarters actually anyway I'll let you think about this one you can read about it in the book yes the thing that makes the horizontal equation and all of these examples actually the right answer for the potential energy yeah the reason these answers are all coming out the exact so far is because the potential is the most quadratic polynomial actually in this case it doesn't come out exactly but approximations to the roots of the area functions you can see in this table before leaving this I want to mention something about multi-dimensional cases the Planck's cell in one dimension as I mentioned is 2 pi h bar that's the area of a single cell if you're at multiple dimensions it has to be a power of this it's a level of 3D it can take a 3-dimensional problem but this is the volume of a Planck's cell in phase space Planck's cells are in phase space so this is actually the 6-dimensional phase space that's positioned in a particle in 3 dimensions the basic rule is that each quantum state occupies a single Planck's cell and I'll show you something let's call the region R let's say that it's volume is capital B let's say that inside this region what we've got is a free particle but now in 3 dimensions so it's Hamiltonian is p squared or 2M but I want to emphasize that the momentum is now a 3 vector like this so this is a particle in a box except we let the box have an arbitrary shape and it's in 3D alright then now let's let N of E be the number of the eigenstates let's name it E naught N of E naught is the number of energy eigenstates with energy which is less than or equal to E naught we can call this the number function the number of eigenstates with an energy less than or equal to an energy I'm going to apply the Planck's cell rule to this and what we'll obtain is an estimate of N of E naught as a semi classical estimate so according to this idea that a single Planck's cell corresponds to a single Planck's state what we need to do is to integrate the phase space volume which is now 6 dimensions d cubed x d cubed p over all 3 positions 3 momentum variables of the region where the Hamiltonian is less than or equal to E naught the value of E naught over here and then we need to divide this by the Planck's cell in 3 dimensions which is 2 pi h bar cubed this is a 6 dimensional integral now it looks like it's hard to do but actually it's not difficult at all because as far as the x in this breaks up into an x integral which is just taken over the region r because that's the only place and then it's times the momentum integral 3 dimensional momentum integral which is taken over the region where let's say the magnitude of p is less than or equal to p naught where p naught is the magnitude of the momentum corresponding to E naught so the E naught is equal to p naught square root of 2 m or in other words p naught is equal to the square root of 2 m E naught so this is easy because the first integral just gives you the volume of the region and the second integral you just use the formula for the volume of the sphere it's 4 thirds pi times p naught cubed and if we put this together we get the the estimate for the number of energy eigenstates and it's equal to the volume to be divided by 2 pi h bar cubed times the 4 thirds pi and then for p naught p naught cubed I'll write this as 2 m E naught to the 3 halves of power and this gets you the answer I can clean this up by collecting powers of pi and stuff like that but this is the basic answer I'll show you the structure of the formula I'm sure you've seen this formula before you use this in statistical mechanics when you want to count states usually they make it a box and they count the number of plane wave solutions of a given energy less than a given energy and you end up with this formula all I'm doing here really is to show you that underwise those counting states is the basic fact that in the base space every state occupies a cell of 2 pi h bar 3 particles although 3 particles makes it easy to do the integral you can just do an applied or any system it could be a good estimate for this number function if you differentiate this to get dN dE this is what you call the density of states the differentiation is easy this is the number of states per unit energy interval which appears in solid state physics in all of the places alright so those are all examples of aspects of the force of a cell okay so this is the all I want to say about WKB theory and semi-classical methods for an answer are there any questions about this before we go on? how do train points work and multiple dimensions? well that's more complicated and when I write a formula down like this we're kind of blowing off the one half we're just thinking that N is large enough so one half won't matter I think that's the simplest answer the multi-dimensional problems are more complicated the classical mechanics are more complicated some of them are inimitable and some of them are not they're chaotic and that affects the whole picture in the days of the old quantum theory people didn't understand that distinction although they knew about integral systems because most of the ones that are soluble it turns out that integral systems have multiple periods one dimensional or somerville rule that's written down already gets applied to each of the periodic motions in the integral system and so in the period from about 1911 when Moore worked out his results for the hydrogen atom Moore really did a one-dimensional problem even though hydrogen atom is 3D somerville generalized this to integral systems in more than one dimension which is why his name gets attached to it as well and so then you get these quantization conditions for each of the degrees of freedom that's the quantization rule in more detail where you take into account turning points and stuff this is a similar approach in which I'm actually ignoring k-shifts but it's an interesting result because it shows you that the number of states and the density of states is proportional to the volume independently of the shape of the container which is something that's going to be quite hard to get by learning the other way because you know the wave functions for a box but if you make it a lobby-shaped thing nobody knows what the wave functions are so this is still correct it's only an asymptotic result but it's still correct okay in the days of the old funk period they didn't understand these spacious returning points because they didn't know about wave functions so they got some answers wrong by this one half the fact that a harmonic oscillator is n plus a half instead of just n was something that took a while but anyway the answers they got were in many cases very good so if everybody knew they were on the right track but they didn't really understand what this quantization mission meant alright so I'd like to turn now to a new topic which is the the elementary harmonic oscillator which we all have seen before so I expect a good deal of this will be reviewed and there's no eraser in there could I cover one up there's no eraser no I can't take it wrong basically what an elementary harmonic oscillator is I say I'm sure I know you to you but I'm going to go through the Rax algebraic derivation of the eigenstates and eigenfunctions of the eigenvalues of the harmonic oscillator which I'm sure you've seen before also but it's an interesting argument and I would encourage you to pay attention to the details of the CFL logic flows Dirac's algebraic treatment of the harmonic oscillator is the simplest and the most famous example of the solution of a quantum mechanical problem by algebraic means what that means is we work with the properties of the operators and their commutation relations but without attempting to solve the Schrodinger equation and we don't do it by solving differential equations and worrying about wave functions based on the harmonic oscillator and also an eigenveminim theory this is really by far the most effective and efficient way of dealing with problems involving harmonic oscillators which you know the one dimensional harmonic oscillator is a Hamiltonian which is p squared over 2M plus 0 to the power of omega squared over 2x squared this is expressing the potential energy potential energy is a this is expressing the potential energy in terms of frequency instead of the spring constant as I expect you to know this is frequently just a small amplitude approximation to a true potential real potentials are never really x squared because they don't go to infinity they have to flatten out somewhere so typically the potential energy is only this quadratic form of the potential energy is only the approximation to a real potential near the bottom of the well another dimension is if you have a multidimensional problem for example if you have two dimensions x and y and the potential energy as a function of x and y has a minimum somewhere like this imagine there's a bowl sitting down like that you can expand the true potential without the minimum and carry out the second order you're going to get a quadratic form this is a symmetric quadratic form and it can be diagonalized by a lithogonal transformation and the result is that the Hamiltonian of a multidimensional Hamiltonian will break up into a sum of one dimensional harmonic oscillators generally with different frequencies the frequencies of the so-called normal loads are usually not the same they may be the same but they're not always but the point is is that the quadratic approximations of the potential in multidimensions can be reduced to the problem of a one dimensional harmonic oscillator looking like this so in solving the one big problem we're actually solving a multidimensional harmonic oscillator as well I only drew this with two coordinates x and y but in some cases the number of coordinates is much larger than that the famous example is the lattice vibrations in a solid in which case the number of coordinates is equal to the number of atoms times 3 and so it could be an enormously large number in that case the diagonalization of the quadratic form with the potential energy amounts to obtaining the normal loads in the vibration of the solid actually this could be considered a classical problem finding those normal loads but once you find them then each one of them becomes a single one dimensional harmonic oscillator which is applied by the methods I would have said in the moment probably the it's actually applicable to multidimensional problems also by the way this is a mechanical oscillator but the harmonic oscillator Hamiltonian occurs in the number of contexts where it's not a potential energy problem for example the particle moving in a uniform magnetic field is a Hamiltonian which can be transformed into the form of a harmonic oscillator another very important example is examples is what happens in field theory in which one field theory which the most of the free field whether they be electromagnetic field or a field describing massive particles can be decomposed into normal loads and each one of those becomes a harmonic oscillator in cases like that the excitations of the given motor are identified with particles and we speak for example with photons the quantization of the electromagnetic field which will very similar to the quantization of sound waves, the phonons and the solid which otherwise is just the normal most of the vibrations in the solid in any case this is just a way of saying a harmonic oscillator has many many applications in physics alright so let's go back to the one dimensional harmonic oscillator and do this there are three constants that appear here a mass and a frequency of omega and it's convenient to avoid colliders and constants to choose units such that all three of these constants are equally one the equivalent way of speaking to this is to say that if you take a hidden value of mh bar and omega you can construct a fundamental unit of length of this equal to the square root of h bar divided by m omega and similarly the fundamental unit of momentum which is the square root of mh bar times omega this fundamental unit of energy which is h bar omega time which is one over omega and so on etc and by choosing units like this it's equivalent to make choosing units of each of these this length momentum energy time that's what are all equal to one of the units that we choose this is going to make the harmonic oscillator now become simply one half mass x square it's a conventional form now to convert back to real units you'd need to multiply or divide by these scale factors to get the actual units to one by the way I can only do this for one dimensional oscillator if I had two harmonic oscillators these frequencies were different I can't set both frequencies equal to one then I have to I can still set in an h particle to one but not to two anyway for one oscillator we can do this this is a quantum oscillator let's say at this point so the commutation relations of the position momentum are that their commutator is i h bar except for setting h bar to the one so it's just i in Dirac's method he begins by defining a set of new operators one is a which is defined as x plus i p divided by the square root of two and at submission contrary at a dagger which is x minus i divided by the square root of two these are the first one is called the annihilation operator or it's also called the lowering operator and the second one is called a creation operator or a raising operator the terminology annihilation and creation was typically applied to photons the quantization of electromagnetic field but the terminology is growing now these two operators are not permissioned so they remember that so they don't diagonalize them on the other hand they have some nice properties in particular let's define a new operator which is a product of a dagger times a well just from the line above this is one half of x minus i p times x plus i p if those were c numbers instead of operators you just both line together and you get one half of x squared plus p squared which is obviously the annihilation but because these are operators there's also a commutator that occurs you see x times i p minus p times i x divided by two so you get i over two times the commutator of x with p so this first term is the annihilation and the second term is i over two times i so it's one half so we can summarize this about only one half over the other side by saying that h is equal to n plus a half the other operator by the way is called the number operator here in the name and the result of this is that the Hamiltonian is the number operator plus a half the number operator has some properties here is that first of all the number operator which is a permission which is obvious if I take the submission conjugate it just goes into itself and it's also the non-negative definite so yeah it is one revision two non-negative definite the fact that it's non-negative definite it means that the eigenvalues of the number operator are non-negative they can be positive or zero it's easy to show that it's non-negative definite because if I take an arbitrary state and I damage it around here recall the definition of the non-negative definite operator is this expectation value has to be non-negative for all choices of phi let's see what this is this is phi a dagger a phi like this this however is the square of the state a phi and the square of the state is equal to zero because that's one of the possible of the of the definition of the definition of the definition alright so it's non-negative definite so the Hamiltonian is equal to this number operator plus a half it's just a trivial change of constant shift the result is that the eigen states of the Hamiltonian states of the number operator are identical and only the eigenvalues are different the eigenvalues of h are just the eigenvalues of n plus a half so we're going to diagonalize n and find the spectrum of the eigen eigen states of n first and then h follows through that curriculum okay so we'll do this in the following way the first thing I want to notice in regard to finding the eigen states and eigenvalues of the n of the number operator n the first thing to mention is that in a one-dimensional problem potential goes to infinity like this on both sides this means that the eigenfunctions have to die off exponentially at both positive and negative acts and as a result it means that the eigenfunctions are non-degenerate they're also discrete they're known as a discrete spectrum of a non-degenerate as we showed earlier in that lecture I gave on the some properties of one-dimensional systems so let's denote an eigenstate of the number operator with a simple nu where nu is the eigenvalue so that n acts on nu and brings out eigenvalue nu now I'm using the simple nu here because at this point for all we know the eigenvalue is the n number positive negative fraction integer or anything else at this point however it's easy to see and the nu has to be actually cannot be negative that's because n is a non-negative definite operator you see from just the line of part so whatever the eigenvalues are they cannot be negative numbers now next let's consider the state nu and I know as soon as this is normalized 2 we'll assume these eigenstakes are normalized now let's consider the state we get when we apply the operator a the annihilation of lowering operator to the eigenstate of the number operator let's take that and let's let the number operator act on it this is the same thing as a dagger a times a times nu now allow me to move the a dagger past the a for which I need commutation relations between a and a dagger which I meant to mention before it doesn't go over here and do it from the commutation relations between x and p it's straight forward without those between a and a dagger so the population and you find the commutator a with a dagger is equal to 1 and so this a dagger a this becomes the same thing as a a dagger times a acting on nu with a minus sign of just a acting on nu however the a dagger a is in the n acts on nu of nu itself so the right hand side is nu minus 1 on point a acting on on state nu like this so we can summarize this we have number operator n acting on a nu is equal to nu minus 1 acting on a nu thus we can say nu here is a an eigenstate of n the number operator with eigenvalue and so this statement says that if we apply the number operator to a nu we get a factor of n minus 1 therefore a nu is an eigenvector of n with eigenvalue nu minus 1 except for one slight wrinkle we have to worry about the possibility that a nu could be equal to 0 because if it is equal to nu nu is normalized but a nu could be 0 and if a nu is 0 then this equation just says 0 equal to 0 and it doesn't give us anything new so to make a precise statement we can say that if a nu does not vanish then it is an eigenstate of the number operator with an eigenvalue nu minus 1 now this raises a question which is does a nu equal to 0 when does this happen when does this happen when does this happen the answer to this will be the basic factor of the space is that a vector is vanish if it only if it is square vanishes so I am going to remove the question mark and say that this condition is true if it only if I take the square of it I get nu a dagger a nu and this is equal to 0 this is how it was the same thing as nu sandwiched from the number operator which is the same thing the same thing as nu times the norm of the eigenstate assuming it is normal I say it is just nu itself so what we see is the answer to win is that a-actuant nu is equal to 0 if it only if nu is equal to 0 and we put a little box around that that is the main conclusion of this so to go back to the formula at the top of the board we will say it again and the light of the new information we will say that if nu is not equal to 0 then a nu is an eigenstate of n with eigenvalue mu minus 1 nu is equal to 0 this equation just says 0 is equal to 0 it doesn't say anything now if we get to something similar with a racing operator let's consider n acting on a dagger at nu this is the same thing as a dagger a with this n acting on nu and now allow me to move this a to the right of that a dagger so here is the commutator of a dagger which is up there and so this gives us a dagger times a dagger times a n acting on nu plus a dagger acting on nu again this is these factors are n n acting on nu brings out nu and the result is that it is nu from this terminal point to this terminal nu plus 1 times a dagger acting on nu so now we have the statement that nu is an eigenstate and not directly with eigenvalue nu so we apply a dagger to it we get a nu state which of it does not vanish is an eigenstate of n with eigenvalue nu plus 1 let's go through the same thing does this state vanish when is the possibility of a dagger nu there actually a dagger nu equals 0 if it only happens square as it equals 0 nu times a a dagger nu however by the commutation relation a a dagger nu is equal to a dagger a plus 1 which is equal to n plus 1 so we can say that a dagger it vanishes if and only if nu plus 1 equals 0 but remember nu is greater than or equal to 0 so nu plus 1 is always greater than 0 and the result is is that a dagger nu never vanishes so we're going to write this a dagger nu a dagger nu is not equal to 0 always so we unbox this part of this well I know so what we've got is that so let's do it this way let's write it this way and say that in happening on a dagger nu it's equal to nu plus 1 a dagger nu and to put it in words a dagger nu is always if nu is an eigenstate of n with an eigenvalue nu then a dagger nu is an eigenstate but eigenvalue nu plus 1 always there are no restrictions alright now from this it follows that the quantity nu the eigenvalue has to be an integer because it's supposed to be a nu not an integer then by applying an a an a squared and a cubed to the nu we get eigenvalue which are nu minus 1 nu minus 2 and we can bring this down up to the point by applying enough a operators we're going to get up to the point where nu minus k is less than 0 well the eigenstates of n don't have any negative eigenvalues so this seems to be a contradiction and the only fact the only way to escape the contradiction is an integer because what happens when you apply these a operators is you're eventually going to get down to the state 0 when you apply n of them and then when you apply the next one a to it instead of getting some state minus 1 you get just a 0 all together that's in this condition here a x and a 0 state here is a 0 so therefore the only consistent solution these sets of relations is that nu is actually an integer which is replaced by n which is an integer and in fact it takes on the value of 0, 1, 2 and so on it has to take on all these values all these non-negative integers because if any one of them occurs you can get all the others by applying raising and lowering operators so if there's any eigenstate at all which there has to be then this is the easily allowed values of integers and so thus we have the spectrum that is the integer 0, 1, 2, 3 and so on and from that it follows meaning that the energy eigenvalues are equal to n plus a half because the Hamiltonian is equal to the number of operators now now I'm going to worry about so now the states so now we'll call the eigenstates n and x on n is equal to n this is the basic relation we're working with here we also have a acting on n is proportional to n minus 1 and we have a dagger acting on n is proportional to n plus 1 summarizes some of the things we learned so far let me call in the first equation we call it a let me call the proportionality constant cn let's say a n actuated it's not proportional to the constant cn times n minus 1 cn is a general complex number to find it we can square both sides of the square the square of the left hand side we get n sandwiched around the a dagger a the square of the right hand side we can guess the value of c n squared times the norm of n minus 1 but we're assuming these states are normalized so that norm is equal to 1 on the left hand side we have a number operator in the middle here and the result is that cn squared is equal to is equal to n just to call the number n therefore cn is equal to a phase factor e to the i let's call it alpha n times the square root n like this so we can now write out some of these relations these annihilation relations here if we apply a to the state 1 we get e to the i alpha 1 times the square root of 1 times 0 if we apply a to the state 2 the annihilation operator we get e to the i alpha 2 times the square root of 2 acting on 0 a acting on 3 we get e to the i alpha 3 I'm just writing down some of these so you can see the pattern this is actually not the case 1 squared and so on this is the information we have so far from these creation annihilation relations now at this point let's take these states 1, 2, 3 and so on and redefine them so as to absorb these phases alpha 1 alpha 2 and alpha 3 and if we do that then we've established phase dimensions for the states 1, 2, 3 and so on for these phases e to the i alpha go away in the process of doing that phase convention phase from state 0 what we are in fact doing is linking the phase conventions for all the excited states to the phase conventions for the ground state and so for that convention I can erase these phase factors and now there's only one phase convention for the eigenstates and that's the basic convention for the ground state 0 and if we do this then I'll draw the result from the little box here it is the result that I think you know is that a acts on n because this is square root of 20 times n minus 1 by a completely similar argument working with the raising operators we find that a dagger acting on n is the square root of n plus 1 times n plus 1 these are relations I'm sure you've memorized for an undergraduate exam at the time so there they are as it turns out it's not necessary to introduce any additional phase conventions for the imaginary equations the phase changes that I made over here are all you need to do and then this imaginary equation automatically follows the effect of these phase conventions is to make the matrix elements of the raising of lowering operators in the energy eigenbasis to make those matrix elements real and that's the most convenient choice to be doing another one and that's all