My name is Connor Goodwin and I'm ProPublica's Interim Director of Communications. Welcome to Race, Police, and Power in small-town America. For those new to us, ProPublica is a nonprofit newsroom dedicated to investigative journalism. In 2018, we started the local reporting network to support local and regional newsrooms as they work on important investigative projects affecting their communities. In 2020, we partnered with the News & Observer to investigate the battle for racial justice in Graham, North Carolina, a small town with a long history of racial violence and aggressive policing and restrictive laws around protesting. For this event, ProPublica and the News & Observer have convened the two lead reporters from the story, local activists, and a historian for a timely discussion on race and policing. We also invited Alamance County Sheriff Terry Johnson, who declined, and Grand Police Chief Christie Cole, who did not respond. Now to introduce our speakers. Don Blagrove is an attorney and executive director of Emancipate, North Carolina, a nonprofit focused on dismantling structural racism and mass incarceration that has, among other things, organized legal defense for Black Lives Matter protesters across the state. Scott Nelson is a professor of history at the University of Georgia. He is an award-winning author who is written about Alamance County during Reconstruction, including in the book, Iron Confederacies. Ebony Pinnocks grew up in Alamance County and was involved in Black Lives Matter activism there throughout 2020. She has also worked in healthcare and public health outreach. Julia Wall is a visual journalist at the News & Observer in Raleigh, North Carolina, where she creates both daily and long-form content for online and print. Thank you to our panel for joining today. Also, this session is being recorded and a link to the video will be emailed tomorrow to everyone who registered. If you'd like to ask a question, you can click the Q&A icon at the bottom of your screen and type it there. Our moderator today is Carly Brousseau. Carly is an investigative reporter at the News & Observer. Thanks again for joining us and thanks to McKinsey & Company for supporting this event. I'll let Carly take it from here. Thanks, Connor, for the introductions. I also want to thank ProPublica, which made this event and the reporting we'll be talking about possible. The News & Observer was part of ProPublica's local reporting network last year, and that meant that I was able to devote all my time to Alamance County and also draw on other resources from ProPublica's newsroom. T. Christian Miller was my editor-in-guide and lots of other people had a hand in the project. A little background on the journalism that brought us here. After Minneapolis police officer killed George Floyd setting off protests across the country, I decided to revisit the Department of Justice lawsuit against Terry Johnson, the sheriff of Alamance County. Some years back, he's been accused of some of the country's worst racial profiling. And I wondered about the lawsuit's legacy. What if anything had changed? And what might that mean for the public debate about police accountability in small southern towns? Deep in the legal file, a government lawyer asked Sheriff Johnson, have you ever in your life attended a meeting of the Ku Klux Klan? Sheriff Johnson answered, no, sir. Well, I'll take that back. Yes, I have. I was in the Greensboro Klan Nazi shootout as an FBI agent. I've done surveillance at Klan's meeting. And then the page cut off. And the next one was missing. And that sent me on a journey trying to connect the past to the present. So I'm really excited to have all of you here for this discussion. So we can continue to make those connections together. Ebony, I'd like to start with you. Given that you grew up in Alamance County. What was that like? And how has your perception of the place and the people changed over time? So, I guess growing up in Alamance County was kind of weird because when I was younger, we kind of ignored the fact that racism even exists. Because as a child, you have friends of alcohol. And as far as you know, they love who you are, you don't know any difference. But as you started getting older, you know, that's where they're starting to act funny. I would say the major point in my life where I realized racism was real and it's the issue right here at Alamance County was one of my best friends in our school. She invited me to her house, but she had to tell me how to act in her house first because her mom was okay, but her stepdad was definitely racist. Her stepdad is also brothers of one of, I guess you could say one of the wealthiest men in Alamance County that owns a lot of stuff that we all support. We've all bought stuff from them. We've all given things. So anyway, I went to her house and it was like one in the bedroom and don't come out and he won't bother. So I'm like, well, she's my friend. She say, I'm safe. She say, and I was, she kept me safe. But I noticed that I will hear the mama and the stepfather arguing a lot. And she was like, well, we're gonna go outside and back and as we move towards the back, the argument kind of gravitated towards that way too.  I can't be friends with her anymore because it's causing a wedge in her household. So that was basically the first time I opened my eyes. This is not a thing that you just see on a movie. It's not dead. Slavery is not that far from where we are today. It's still here and that was, that was a big wake up call because I look at it right. How did you start to connect that experience with policing or what brought you into the streets? Can you talk about that connection? Well, the connection for me was I have children that are younger books. One is that was some state and I have one that's out on his own and I can no longer protect. I cannot protect them physically because they're not in my home. The only other way I felt I could say never was to actually get out here and start fighting. Start trying to be part of the solution instead of the problem because by not doing anything, I'm part of the problem also. So I had to start because I hadn't really been educating them on racism either because I felt like if you just stay in your lane, they'll stay in theirs and we never cross lanes. We don't have to worry about you because that's how I grew up. But then I mean just realizing how you remember your best friend, how that worked out like let's go ahead and do something about it. So that's what ended me in Brown last year.  That was the big thing for me. Dawn, does this resonate with you and what you hear from other protesters across the state? Yes. Yes, it absolutely does resonate with me and I just need a minute because so very often we glaze over the trauma that racism causes to black people in America and especially to our children. There is this pre-just a position that our children and that black people should just be able to absorb these traumatic experiences and should never have the space or the audacity to think that we should be able to discuss the trauma of those events and acknowledge how hurtful they are and how they create generational trauma. So sorry, I just needed a minute to sit in that. But yeah, these are very similar stories that we hear all over the South, the South particularly, but especially as it relates to black folks who are born and raised in the South. There is just a certain unspoken set of norms that relate to how you interact with white people in your community and how your age absolutely determines what the rules are, right? And that is a reality that people deal with all over the state of North Carolina. And yes, I have children. I have two daughters myself. That is what drives me to do this work. And that is what drives most of us to do this work. And that is a reality that people deal with all over the state of North Carolina. And yes, I have children. I have two daughters myself. That is what drives me to do this work. And that is what drives most of us to do this work is that we do not want our children to have to fight and validate their humanity the way that we have to do over and over again. So, yes, what Ebony is saying to you is absolutely commiserate with what I hear statewide and nationally to be perfectly honest from people who have decided that now was the moment, especially in the wake of George Floyd, that now is the moment to become active. Now is the moment to say, I will no longer accept second class citizen. You mentioned intergenerational trauma which sort of brings us to the idea of history and I mean that's, I think, in many ways that shared across geography but also can be specific to geography and I'd like to turn to Scott for a little of his work on on the history of Alamance County. I know that Scott you've done a lot of work about Wyatt outlaw and that's a name I heard a lot in the streets in Ebony's mouth and many others. When Julie and I were out there so could you tell us about Wyatt outlaw and and how you see that story kind of translating forward. Wyatt outlaw was put to use dawn's phrase, the kind of peak of audacity, right he was somebody who pushed back against all of these ideas about what was acceptable for a black man to do right so he's in the US colored troops it's called in the Union army. And he fights, you know, alongside white soldiers against the Confederacy returns to Alamance County and he's the town constable. He organizes a group called the Royal Republican League of black men to and men are only the ones voting at this time to get them to think about voting and think about their citizenship and take pride in themselves and who they are and. creates a kind of peace he's friendly with both, he's biracial and he's friendly with both black and white folks in Alamance and the powers that be like Ebony is talking about are not happy with us. And so they, they organize the client and they, they attack him once in 1869 and. And then again in February of 1870 where they, where they hang him where they kill him where they where they beat him up in front of his six year old son and his mother and drag him to an elm tree and hang him in the center of of Graham and so that that the sort of heroism that took him to do all that to stand up for everybody in that community. But particularly black people in that community, it was was amazing and and it's he paid the highest price for for that audacity and recalling that that not just his death but the audacity to sort of stand up and fight, because I think what's exciting about the story of Ebony what did you think when you first hear that heard that story. When I first heard the story. First of all was what break into that it was the first time I heard it. To be someone black and from elements can you know nothing about yourself. It's kind of crazy. But when I first heard it was just. I don't know what we've always been here, and for there not to be any classes or anything in history but when we go to school to learn about this stuff right here in our own county, it was my role. I mean, Julia you've covered protests in a lot of places. It seemed to me with less experience and then you have that the history was coming out more often like what, what did you observe what jumped out at you about the experience of being at protests in this place compared to others. Yeah, I think that the big differences this very localized narrative and collective history that had been ignored for so long and people. They got together in order to have their voices heard and then perpetually still being ignored by people within the community by people in the local government by people in law enforcement that the reasons that they were there weren't really being heard and why it outlaw Although it became more popular within within the groups of people who were who were showing up to these protests, it was different from other places, because there was such a stake in in resurrecting this story for people who live there and grew up there and like being able to learn this story for the first time was a very intense experience and more and more people were learning about that in these at these protests. And, you know, kind of as the dust settled per se in the winter, there would be more focused events through groups like occupied Graham where they had a whole night dedicated to why it outlaw and they had made pamphlets about him. So it was just a much different take away and kind of concrete thing that came out of these, these events rather than events taking place in Durham or in Raleigh that were, you know, bigger cities and there may be bigger crowds but this story kind of tied everybody together to this place and even people who weren't from Elements County who were coming in to to attend these events, we're learning more about it and just kind of perpetuates the story and get brings it out to more people than I think have had ever heard it maybe. Don I can see your comment about this kind of history the story of why it outlaw being intentionally suppressed and that being part of systemic racism can you expand on that. I just think that it's so important that and I hear Ebony saying, and it's a part of living in a system and in a country that is so oppressive to us that we internalize so much of their oppression, as if it is ours and that it is ours to own and it is not. It is not your fault that you don't know who outlaw was or you didn't know who he was, because it is intentionally suppressed from us, because the people who have power. Understand that it is in their benefit it is the benefit of upholding white supremacy it is in the benefit of upholding systemic and institutional racism that they do not tell an accurate depiction of the history and the role that black folks played in that history, especially in places like Alamance County right, and which is ironic because, as we taught as we moved to talk about these Confederate statues, these folks are so so deeply rooted and committed to history to preserving history. Right, as they if you let them tell it, but we can't be gas lit by these non racial non racial. Excuses for sanitizing racism and hatred because that's really what this is. And I think that but again, it is not ours to own that it is not our fault that we don't know these things you know I do train is all over the state about the roles of district attorneys and judges and sheriffs and people will say to me who are who have been politically active their entire lives. I'm embarrassed that I don't know these things and I said oh no don't be embarrassed, because the power of the system part of the way the system holds on to its power is to obfuscate this information. There is a very, a very intentional and a very intentional and deliberate exclusion of our stories from American history and it is American history. It's just not the American history that they want to talk. Scott I know you were really taken by one of the signs that that I think Julie also recorded at some of the protests in Alamance County, especially late last year that said Google wide outlaw. I'm glad to hear you talk about that and also, you know, how in your work you found that this story or the, the broader history of kind of what wide outlaw was doing and, and his, his fellow. The people who was working with an Alamance County, what they were trying to achieve and did achieve how that story kind of got vanquished to us. It's the, in fact, just as Don saying that there was a tree right where he was hanged and people knew where that tree was in the 1880s and 1890s and then the tree fell down. And what did they replace the tree with, but a statue of a Confederate soldier who wasn't there, right, right, the man who stood to defend Graham. Right, was out was wide outlaw. He used to defend the town against these plans man. And when his memory goes away from the people who remember it, it's replaced by, you know, a marble Confederate soldier. It's a, it's a horrible thing. And what outlaw wanted to do was to create a kind of multiracial democracy that was that was what he saw he, he made friendships he was a carpenter. He made coffins but he also made, he built the house that he was in, and he did a lot of building for the North Carolina railroad and he wanted to create this this multiracial democracy at that time headed by the Republican Party, the Party of Lincoln, and in which black and white people stood together. And when he was killed the governor Holden at the time overreacted in the, in the sense that he sent in troops. And that was, it was the right reaction to send in troops and to capture these people. But the result was that people that white people got scared when they sent in troops after the people who hanged wide outlaw. And it broke apart that democracy people. It drove people white people into the Democratic Party the party of the Klan's been the party of the old Confederacy, and help crack apart that multiracial democracy that very brief multiracial democracy in North Carolina 1865 until, until 1870. And, and when it broke in North Carolina broken the rest of the south that was, this is the center of alamance, right, which is the center of North Carolina, which is the center of the south. He stood by and kind of built help build that that coalition. And when they killed them, as they did many other black leaders in that period.  So, anyways, that's, that's my sense of how, how in the, in the sense of what's happened in 150 years ago that's why we have to remember it is because it's, they want to cover those tracks of the people who were trying to build something that was, that was a different kind of North Carolina and different kind of south. One of the things that happened in the course of our reporting is that there was also an effort to kind of reclaim white outlaw as a member of law enforcement and that was. Well, I guess that to some degree proceeded our reporting but Julia went to an event in which he was actually memorialized. Could you talk about that a little bit Julia what were your observations. Sure. There was a fallen officers event in, I want to say it was in early May in Alamance County and and there's like I think it was during National Police Week. And they had had a similar event that is also on the county's YouTube page because they they uploaded it to their YouTube page when they did the ceremony last year, in which they for the first time in the country's white outlaws name into the fallen officers memorial for Alamance County. And what's interesting, a lot of people don't know about white outlaw and maybe Scott could speak more to this because my knowledge of it. Why is very limited but there aren't any existing photos of him. But if you do a quick Google search a photo of another man pops up in relation to white outlaw and that is the man whose photo is printed. It's in a very big frame that is carried and placed into this officers memorial now for two years in a row. And it's not why it outlaw. It's, it's, I'm the man's name is escaping me. It's casual. Yes, it's casual hold it's not why it outlaw and for two years in a row now they have presented it as why it outlaw in these fallen officers ceremonies. And also, like, kind of tangentially like saw a conversation on Instagram going on when the local History Museum had put up a new exhibit and they didn't include why it outlaw in it and people were very upset about that it just feels like this information is now very much in the public sphere and the fact that that's casual hold and not why it outlaw has been missed on the folks bringing these photos to these ceremonies. And what else has, has thoughts on that kind of like the shifting legacy of white outlaw. I just want to ask the, ask the professor. Holt is one of the, one of the leaders of the clan at that time what is who is this person that they're showing us. No, no, no, there's, there's multiple holds. And so, so hold is the name of an old planter family. And so there were white holds and black holds and this was a black hole that was that was the image was of, and he was, you know, this man was did know why it outlaw he actually he didn't see the murder but he shots were fired at him. But the name hold comes from because he was owned by, you know, I'm going to, I'm going to, I'm going to tap down my outrage now then. I was like, wait a minute, what. No, he, but hold was I outlaw it's difficult to know what he looked like but he wasn't wasn't as dark as the as the man who they use in the image and yeah he had a mustache I think and he was he was sort of. Yeah, but but it is a shame that that that's it's funny because the thing that's been perverse about the 150 years later is that white outlaw was the head of the police right he was a town constable he was a person hold he was a person holding that town together right. And, and then he was killed and 150 years later that's not what elements looks like right that's not what Graham looks like as I'm sure. Ebony can say that that what we see in elements of policing is in different hands, and people are in danger in part because of the police. So Ebony, maybe you can kind of take this up to the present, like what are perceptions of law enforcement in Alamance County now. Well, um, first of all, they're not here to protect and serve. They only protect certain people, just from being in the streets. The Confederates, they could get in our face yell at us, fitted us, put their hands on us, they could do whatever they wanted to. It did not matter they could say what they wanted to. The police would not bother you, but you know, as soon as we say anything, we, if we say a curse word all of a sudden, we're wrong, but they have called us the N word. They've talked about our children. They've done anything, everything they could standing right there in our face.  I mean, I had heard it heard it spewed before, but not directed towards me.   And they didn't know. But if we stepped up sidewalk, we went to jail. If we didn't move as soon as they told us to, we went to jail over with pepper spray or our children were being toppled over by police. Where the other side, they could, they could stand on over the bricks and hooting holler and outside with alcohol doing everything they wanted to. And they wouldn't do nothing but protect them. They would protect them every time. We've seen one arrest. I think, and they literally took the person around the corner and let him fall. What does that make you think, Don? I mean, it's, I don't know.  Like we go out there and we have those difficult conversations with people that we would never talk to because we're human beings too. And if you don't like me, I don't like you, but I'm no better than this. I know that we, if we talk to each other, we can coincide with each other and be okay. I know this.  The people who you can't talk to, they don't come out there. So this is your chance.  We can have good conversations, but then here comes the police who batch and that's when everything starts to change. It's not the conversations that we had with each other as the community. It was when the police got there is when they started a certain being aggressive for no reason, starting stuff, inciting riots, because we would be calm. We might be yelling and fussing, but I mean, it's something that we're all passionate about. They're passionate about their preserving their history and we're passionate about being part of it. So it's like the police is the one who calls all the problems. So Ebony, I just need to jump in right here because what you're saying right now is so important. And it's something that so many people who are not on the front lines don't understand. Here in Raleigh emancipate and see was one of many other organizations in a coalition called. Oh, I can't remember the name of it. I'm sorry, y'all, it's been a long day. But Raleigh demands justice. Lord have mercy in a coalition called Raleigh demands justice week where we posted a and helped organize a large protest on May 30. In response to George Floyd's murder. My oldest daughter who was at the time, 20, I think, had never been to a full blown protest like this before. And one of the things that she took away from it was this is what she said to me when we got back in the car and it hit me like a ton of bricks. Mama, I didn't realize that police started right. Right. And if you're not out there, you don't know that it is the police that very often are the aggressors that are the people that antagonize and bring violence and bring hostility to a place that is really there for where to a place where really we could have a meeting of the minds where really people could have some real powerful exchanges of ideas.  Again, that doesn't happen by accident. There is absolutely a reason and you nailed it. The reason why law enforcement's it is used to put this wedge between the two sides because what they know for sure what the system knows for sure. Is that if these two sides were able to talk, what we would find is that we have much more in common than we have not in common. What we would find is that if we were working together towards a common goal of community safety and advancement and economic support that we will be so much more powerful that my friends is what they want us to not do and make no sense of that is exactly why law enforcement municipal law enforcement in America was created. It was created not about safety or community, it was created about to maintain social norms, and those social norms were the ones that uphold white supremacy and oppression of black folks and were to advance the stereotypes, the myths, and the misnomers that exist to keep white people and black people, or white people and brown people, not talking to one person and not having real dialogue. This is what systemic and institutional racism looks like, and this is how it exists and this is how it shows up in our lives. And law enforcement is being used as a tool to advance those oppressive systems. And we've got to be able to name that and call it when we see it and Ebony you you killing it tonight girl killing it. I think it's back in time a little bit it seems like we've talked about why, you know, the, the death of white outlaw the killing of white outlaw setting in in motion what follow, could you kind of, I guess set that up for us. And thinking about what's almost saying about maintaining social norms, right. And, and so there was a, there was a way of policing before the Civil War and the way of policing was the basically you, you'd call on white people poor white people to act as to round people up, right, to chase after enslaved people that had disappeared to, to, and so the enforcement of social norms was very informal. And it was, it was get a patrols called the patroller system. And when people were interviewed by people were interviewed the 1920s they called the Klansman the patrollers, right so referring to that old system of social norms, where black people did one thing and white people did another and, and quiet out let's try to break that 150 years ago 152 years of 53 years ago, by, by creating a police force that was the town constables that just enforce the police just enforce the piece, right. And that they could not stand that they could not accept that they could not abide by that. And so they broke they waited until on February 26, they, they came in that midnight and, and shot and killed him. They tried to get Caswell Holt but they they went to outlaw's house first and Holt discovered it and he got out he was able to escape but, but they were trying to eliminate all the constables right everybody who was part of a system that was not their informal social norms that was the thing they tried to break and they broke it on 152 years ago, and they brought back the slave patrols, and they brought back those social norms that, you know that had been briefly extinguished for a few years. For a few years after the Civil War. And so we don't know about that time because, you know, all the effort is event about making that go away and that's the funny thing about the police kind of claiming white outlaw to as a fallen soldier and you know fallen fallen officer or something like that, because the kind of police that he represented was a police that was really about law and order that was really about protecting everyone in that community and that police has gone and it's been gone for 152 years in Alamance County. And I just very, very quickly because there was so much that I wanted to add in this conversation, but I most importantly want to say that today in Raleigh house bill 805 past mostly along party lines, the house, and that isn't the and anti black lives matter anti riot protest bill right it is on its way now to governor Cooper's desk, and it is imperative that everyone on this call, call Cooper and tell him to veto this terrible piece of legislation, and not only do I want you to call and tell him to veto I want you to tell other people to call and tell him to veto, because again this is what institutional racism looks like, and this is how it becomes part of our systems when you create laws that on their face, look as though they are race neutral, but based on what Ebony is telling us about what is happening in Graham County is that she is being called racial slurs, they are being the black lives matter protesters are who are who are being peaceful, who are being who are protesting and exercising their constitutional right to protest are being treated as though they are an eight lead criminal, whereas those folks who are actually displaying hateful criminal behavior are being given a pass like in the video that like in the documentary that was produced, where the black lives matter protesters one of whom was I remember just trying to go across the street and get food was treated so roughly. And a white protester was arrested, not dragged up the steps of the courthouse, but taken into a restaurant, a place that was much less, much less confrontational much less stigmatizing as it relates to to being justice involved. This is why it feels like these that are burst out of racism no matter what they want to say, and no matter how race neutral the language is, this is why we have to stop these types of legislations from more deeply embedding racism and bias into our systems and last thing I'm sorry I was quick and I lied. We need for people that don't look like Ebony and I to say that. Right. We need for you. Because until white folks decide that this system is egregious that this system is one that is unworthy. It's unworthy to be called American. Right. And they turn on it and demand change. Not just because they have skin in the game but because it is the right thing to do. Until that happens. Ebony and I will continue to be in the streets and yelling and screaming and protesting and demanding our humanity be recognized.  Don't care what we think they care what you think. One of the things that I thought was particularly powerful, witnessing what happened in Graham over the last year was that there was kind of a physical embodiment of of some of what you're talking about Don of it was we were talking about the physical public and access to it and equal representation within it, whether that was through monuments or just physical presence. I know that there have, there has been other legislation as well that sort of touches on some of some of the issues that came up in Graham and in other cities. In the post George Floyd in the bill that you're talking about. There was an effort to make to increase the penalties for being present at what is deemed a riot. And so those those the sort of definitions were in flux and expanded. There was another bill that I thought was interesting that came up a few months ago that was proposed by Senator Amy Gailey who was the chair of the Alamance County Board of Commissioners and that bill related to disruptions at public meetings. Julie, I don't know if you want to describe the public meeting that we went to where where folks were trying to get in and and sort of what your observations are about. Sure yeah and and Ebony was there as well. I can't remember if you came inside Ebony but I know you were outside the courthouse that night as well. You did come in as well yeah so I'd also like to hear your take on it because mine was very much focused through the camera, but what I saw was a board of commissioners that was threatened by the presence of activists in their public meeting and it was the first, first opportunity to make public comment in person after what happened on October 31 and almost immediately upon people entering in order to settle down and into the room and wait for the public comment section. There was an altercation over where to sit because of social distancing and several officers in not riot gear but in full vests came out from wherever they were, and kind of postured at everyone, and then I left the room and and some some pretty awful events happened after that on and the elements kind of sheriff's office do not wear body cameras so we could not see those arrests and full after the fact but Ebony what was your experience like that night. So, I think we had had a little press conference steps before we talked or something like that, if I'm recalling it correctly, and then several of us started to try to go in. We had certain stuff on us that we can bring that in can bring that in so they were already harassing the start of the tears from coming in so once we got in we went upstairs. And when we walked through the door, everybody in the whole room stopped talking. I can't remember who was speaking at the time at the podium but he looked like he's saying several ghosts. Everybody turned around and started looking at us and we just, we made our way to our seats and we were the first group in I believe so we were super people quiet, but downstairs, we can hear a lot of ruckus. I'm not quite sure what it was, but it was important we got up and started down the stairs to calm them down because we didn't know exactly what was going on. Eventually, that crowd made it upstairs and that's when the arrest started so I didn't see that myself, but I just know just to go in there and sit down and be quiet. They let us know we weren't welcome. You can tell the conversation changes every time we step in the room. So that was one of those things where they kind of stopped looking at the paper and started looking at us. And the meeting is not for us so read your paper, but they stopped. You can tell the whole conversation change when we got in the room. I mean, what one of the things that makes me think about is this question of sort of like, what is real and how video has come to help us define what is real. And we're now some of the reporting that we've done since the story published is about gaining access to law enforcement video. And we've had a difficult time doing that there have been a lot of issues related to law enforcement agencies, having video to start with as Julia pointed out the sheriff's office. Well they actually said in a court hearing that they would never have body camera footage that was what one of the attorneys said. Grand police do have body cameras but that has not in every case been turned over to the district attorney, or in some cases to the judge when there is a petition for for that footage which is required in North Carolina. Under North Carolina law you have to petition a judge in order to see that footage in many cases, unless you are requesting as somebody who's represented in the footage itself. And that's another thing that's also being debated in the legislature right now so at like in conclusion, I would love to hear you all talk about kind of how in this moment now, we move forward to to define kind of like what's real but how does this get back in the public square in the public debate in a way that's productive or possible. I'll jump in real quick. So first I like to say it's kind of weird, and it's hard to approach anything. If I didn't know you and I see you in the store, like I'm a really happy person I speak to everybody I don't know if I can speak to you. And like I see other white people looking at me like I want to speak to her, and they don't know if they can speak to me. So, I don't know. I guess the way it's just been placed between us as black and white people right now we're going to have to have those difficult conversations and for that wedge back out because before it wasn't necessarily there. We've had to face reality, and we have to just deal with it so we've got to be able to talk to each other without the politicians and everything else and it's just community members and get it back on track because it sucks not knowing whether it's okay to be your neighbor's friend or not. That's beautiful Ebony and I think also but again, like I said Ebony is bad and a thousand tonight y'all because really this is about reimagining what it means and how we change systems. How we dismantle system. What we have to do is give ourselves permission to think outside the box about the way that we interact with one another about the way we talk to one another and about the way we relate to one another. Okay. And when we do that when we don't allow these racist systems to dictate how we communicate with one another, how we interact with one another. Then we get to the place where Ebony is talking about where we can have these real genuine conversations where we can listen where we are, we are not so deeply bogged down into ideological tribalism. And are more interested in talking about our day to day lives because let me be real. Most of racism is a is a is a terrible terrible mechanism to help control capitalism and help control capital. Right. So what we have to remember, especially now in a time of COVID where poor people. I don't care what you look like poor people are catching it right now, and we'll continue to catch it. And the one thing that they don't want is poor people talking to one another. Right.  Right. And that's what they want. So we, we have to, we have to untether ourselves from traditional systems of interaction, untether ourselves. And our thoughts and our minds from parties from political parties from, you know, identities and things of that nature. And really think about what makes us more alike than not alike. And when we do that, that is a powerful thing I tell you what though you be careful. And that's what got Fred Hampton killed in Chicago, right, was bringing together people who had common goals and seeing beyond the artificial barriers that are created to advance economic to advance capitalism in America. That's what we got to do. That's the next step. Okay, I just wanted to, I was thinking about the public square, Alby and Terje, who is a friend of white Alice, a white, white friend of white Alice who were novels, and put put outlaw in the novels. He said that the biggest problem in the south is that there aren't town meetings, the town hall meetings that you see in New England and Midwest we don't see them in the south. And he said, without town meetings. There's, there's no dialogue and so that ebony walking in with other with other black people right in that town meeting, and everyone's shutting up all of a sudden because this is not for them. That's that speaks to exactly this problem that that we need a kind of town meeting right and that's what that square is about that's why that square is there. And putting up a fence around it around the Confederate monument is just breaking up that public and we need a public we need a public place where we can we can hash these things out and and not have provocateurs which is frankly what the police were in this case. They were Asian provocateurs they were there to make trouble so they could, you know, beat in heads and stop it. And so, seizing the public square and to and making it a place where people talk to each other is, is I think the thing that's missing in this in the south. And, and that's, that's where the healing is going to be and I and I think town meetings. Part of it is just showing up at those town meetings and recognize it's just not for those people. It's for it's for all of us they they're there to represent us and if there's not enough space there. That's their problem. And the reason there isn't enough space is intentional y'all. I do want to also just uplift as we talk about coming together and having these community dialogues outside of the the norms that are created for us. I am actually involved very deeply right now in a in some litigation that's going on in alamance around where where some black women who were participating and who were courageous enough to speak up and speak out against a person who they believe said some really horrible things, and is in a position where she is being trusted with the lives of folks right. They spoke up and spoke out against her, and this person is using the alamance legal system and the innate racism that is baked into them to bring a defamation lawsuit against these black women and using your legal system to terrorize them and to make them fearful and to bully them. So I'm going to ask you all to come out the week of October 4 to that Confederate statue that stands on literally on the courts of where justice is supposed to be doled out and start having those conversations. You all come every day the week of October 4 and have conversations with one another about the way that alamance county is using your legal system to further racism to further hatred, but most importantly to silence the voice of the people. October 4 y'all I hope the week of October 4 we hope to see y'all out there having these good conversations. Let's expand our questions to the audience and see see how we can in this most immediate sense. Yeah thank you all for the very lively discussion and for the robust number of questions submitted. We'll try and get to a few here. So I'm going to start off like a lot of you are talking about the importance of finding common ground, and that as a starting place and what you know one one person asked if there are any instances of that happening like while you are out protesting or just in the course of your work where you know you did find some common ground to connect with other people. I'm jumping. Absolutely. We've had a lot of hooking up. We've sat down and talked to some people who necessarily went and talked to us and we made a lot of groundwork with them and just came to a conclusion that we all want to protect who we are.  And so we have made friends and people that we keep in contact with that was on the other side. And they're not working on their family and I'm working on my family because that's how it's got to work. We got to pass it on. So it has been some good conversations coming.  I guess that's me again. Honestly, I have kind of pulled back from protesting myself. What I do is build a community. We have these community events where we go to some of the four areas and we might have a cookout on depending on what is going on at the time if it was getting vaccinated or whatever. We just basically build rapport and then whatever we have available that we can help build these communities up. We present that to them because otherwise they may not get that. So you might not want to protest. It's not everybody. Everybody doesn't want their face out there. But there's just several things to do within the community. It's different organizations that I always donate to. We always need water and stuff to protest in different places. It's a lot. You don't have to be on 4th Street. What are the names of the organizations in Graham? There's several. You do have occupied Graham. They have food boxes in different areas. They have one on Washington Street. They have one at the Muse in front of the Muse in Graham. You can donate. My parents should be good. It's there. You can also go in the Muse and donate directly to Dion. She's the owner there. Anything that you donate to her definitely gets out to the protesters and to the community or wherever it needs to go. So that's like a great spot to go to if you want to donate. And also, y'all, the most powerful thing you can do is use your personal influence within your sphere of influence, right? You don't have to do some grandiose gesture. The most important thing you can do is have these difficult conversations with the people in your lives, with your coworkers, with your friends, with the people that you go to church with, and help them to challenge some of the things that they believe to be true. Help them challenge and break up some of those norms. The most powerful thing that any of you can do is talk to your own people. Talk to people around you and help influence people around you. I tell folks all the time, I can do lots of protests and blah, blah, blah, and lawyer in and all that good stuff. But the most important thing I will ever do is raise two daughters into adult women who believe that a better world exists. That is the most important thing you do. Create better people for the world. You do that by talking to folks. One more question for the journalists. So what was one of the most difficult parts of the reporting process for this story? And then someone also asked to Julia specifically, as a visual journalist, what did you feel was most important to include in the visual telling of this story? I'll answer that one quickly and then I'll pass the other one off to Carly. I think one of the most important things to include in visual coverage of a story like this is as many sources of video as you can find and get permission to use. I watched lots of Ebony's Facebook Live videos and other people who I became friends with on Facebook over time. I think that being there a lot of the time and talking to people and putting our faces in kind of people so that they knew who you were was incredibly important for both parts of the reporting. But piecing together different perspectives of things that we were trying to report and improve a point with about what was actually going on there and the truth there I think is one of the most important parts of visual coverage. I think the answer is quite similar for me. So, it was clear to us sort of early on that to tell this story completely and with as much like fidelity to reality as we could we needed the trust of people on the ground protesting and that did require being there a lot and listening a lot. It required building trust and listening to people who were counter protesting and that was that was hard to find access points right to be able to represent that perspective. In a way that they would recognize it all which was I think important for the credibility of the story that that also took a lot of time and a lot of background research I mean there's so many interviews that are not in this not represented in the story itself just like hundreds of people in the community to understand a small town that doesn't necessarily like outsiders always or to be portrayed by outsiders and you know we took that seriously and then the third component was this law enforcement component which also has felt misrepresented by the news and observer and other media outlets in the past. So that was really the hardest thing was building trust and a lot of the solutions that was an incredible investment of time to try to really understand. Yeah. Great. Well that's our time for today. I just want to again thank our panelists, you all were great for this excellent conversation and our moderator, Carly Bruce so thank you to the audience for joining us today and for your thoughtful questions. Again, this event has been recorded. So you'll receive an email tomorrow with a full recording of today's video. We will also post this on our YouTube channel so you can share it with friends who might not have made it from all of us at ProPublica. Thank you for joining us and have a great rest of your evening. We'll see you next time.


th their employees or to have some sort of subsidized childcare for those days when You know the kids aren't in school and the parents have to work Um, so basically I'm just maybe planting a seed if anyone thinks of something that we could do to help advocate for something like that at a state level um That's really kind of where my thought ended But it was just that this problem is bigger than us and I hope it's not on Us meaning the schools and the community built around the school to solve it all And I've gotten some emails that were directly to me not not necessarily sent to the full school committee along that same dimension About you know, can the state, you know support child care or other other uh other ways they can do that So, you know, the other people are having similar thoughts to you as well That's there and then miss lord I share your concerns and I unfortunately everything I've been seeing is Child growth going in the opposite direction that we may see a contraction in the number of slots available for Um younger children at least so so I mean, I guess this is the question, right? So Um How where what are the levers we can pull in order to solve this problem? And I think it's unfortunate that at the time when that we're going to have the greatest need for some of these Things like funding for the PPE and you know more childcare slots for parents who who newly need them Those things are not available So I don't have a solution, but I wanted to Yes, this is um just about the survey I didn't understand that it would be public and I don't know if other families felt that way So I don't know in the future because some of it feels very, um Personal and I'm I want to be protective of that Not that I don't trust our community at large, but I don't know if there's a way in the future to you know, suggest Being more anonymous or finding ways to make it more anonymous just so that We protect our families Yeah, and I if I could respond to I I'd love some thinking about that I mean our community in the past has really um desired for survey results to be shared In the raw format they were we typically Look for survey results and scrub anything that identifies a name a teacher name a student name This was a hard one to scrub was long, but I think we got it If anyone noticed something, please let us know um But I think maybe a proviso at the beginning that all responses will become Will be shared in a public document would would perhaps be more explicit about that. That's great feedback Right because I do I also hold that let's be transparent, but I also hope the this information or why not want to share Miss uh generally so along the lines of um Making sure that families in the community are representative and maybe there's you know employers being flexible I think as a district that employees um You know many teachers that have children that are going to be need needing to be flexible You know, let's keep that in mind as as a district as well that um, you know for those that have Young children that are going to be on a split schedule No matter what it may be that let's think about how we can be flexible for those people to maintain employment um specifically if they're in different schools then You currently work in and one other point. Um I lost it. Sorry. I forgot No, I think it's a great point And I think it's one of the things that I find frustrating about the state's school choice law It's different in other states, but in some states, um right now in massachusetts The only way only uh folks who are prioritized in the school choice list have siblings having in the district um It has always bothered me When I was a staff member a teacher and didn't have kids It just philosophically bothered me that we weren't allowed to prioritize staff members who work in the district on school choice lists That's the law. Um, I think it's um unfair Said this before in public meetings. I think it's unfair that we're not able to prioritize staff members Especially as we live in in four communities that are on the more expensive side um of in western massachusetts So so that's really bothered me and um, I don't have a good solution for that. That's not changing state law, which Isn't easy But I do think when we think I mentioned before about child care for for staff members At least offering it and trying to think about how we could do that safely and and reasonably Um, we are going down that road and trying to think about it. And I think to miss seager's point I hate to be pessimistic again about this But I do think it's going to be on the schools to solve that problem Even though I agree it's a much broader problem than what we have And so we are trying to think about given the survey results. How do we maximize? Uh what we can Uh in terms of in class time for elementary kids while taking that feedback This is just my perspective while taking the feedback that we need to get every secondary kid in The district and so we're working on models to try to do that. Um, again, it's it's a puzzle piece There's some some pieces missing in terms of transportation and staffing That we have to wait and see but that is what we're trying to find the right balance of But I I am not optimistic about the state Jumping in and offerings. There's no evidence that uh leads me to believe that that will occur I'll put it that's a more appropriate way to say what I want to say Any other Comments and questions If there's not I just want to say I continue to work closely with with the miss called superintendent colkeen in union 28 And we continue to chat and text. Um, including tonight And um, you know, because we I do know there's a cross section between what happens in union 28 And this these three districts as well and not that we have to make decisions for one another That would be inappropriate But at least that that line of communication continues to be open I want to publicly thank her for always keeping me in the loop things going up on uh, Up and she's very clever Okay, thank you Okay, so, um, it it seems we'll we'll talk about scheduling our next, um Big joint meeting, um offline but tentatively coinciding with the region school committee date, okay Um, so with that, um, I will entertain a motion from The emmer school committee Who's your adjourn? Second Moved by demling seconded by spitzer. There is no discussion vote. Um, uh, roll call vote. Mr. Demling Demling I Miss spitzer spitzer. I Mr. Harrington Harrington I Miss lord Lord I And mcdonald I I'll turn it over to miss hall All right, I will entertain a motion to adjourn helms will committee meeting So moved Go ahead second All right, uh, okay roll call vote ron Manino I Jesse John Louis I There best Kenny I Margaret Stancer I and haul I Okay Um, I I'm gonna now turn it over to mr. Demling Okay as chair of the union 26 school committee seeing the presence of a quorum I will call to order the union 26 school committee And before reading the following Motion, I will do what is required of bodies meeting virtually which is to go around And ensure that we are present can be heard. So, um Going to scratch my head here because it's been a few months since we've all met it's union 26 So the union if you are a union 26 member, this is going to be Um, is this miss mcdonald miss mcdonald? I think miss. I think miss spitzer is the other emersed. Okay Um, let me hear miss mcdonald miss spitzer. Um Um Present Okay Uh, and then the other three members of union 26 miss hall. Yes hall president. Um, mr. Manino Manino And the sixth and final member of union 26 is It's either miss dancer or miss seager I believe no Dr. Morris is it possible the sixth column member cycled off and we have not replaced them I'm going to defer to the chair of pellum here. Um No, it's just it's um me ron and margaret So, okay, so miss dancer. Yes It's cancer present. Sorry miss dancer. Okay Um, okay now we're in the workout session and so, uh, if it's okay with the regional chair, I'll read the union 26 motion first and then Have you read yours? Is that Okay, um So I move that union 26 enter into executive session according to mass general law section 21 Chapter two to conduct strategy sessions in preparation for negotiations With non-union personnel or to conduct collective bargaining sessions or contract negotiations with non-union union personnel Dermene cunningham assistant superintendent If an open meeting may have a detrimental effect on the bargaining position of the public body And the chair so declares and I do so declare With no intention of returning to open session Is there a second on that motion? second Moved by demlich seconded by miss mcdonald's roll call vote to enter into executive session.  Menino All right, you point six is um in executive session Um and for the region Um, I move that we the region enters into executive session according to mass general law section 21 chapter two To conduct strategy sessions in preparation for negotiations with non-union personnel Or to conduct collective bargaining sessions or contract negotiations with non-union personnel during cunningham assistant to superintendent um Should I continue? And and continue in exact after union 26 adjourns With no intention of returning to open session the region will continue an executive short Session in accordance with mass general law section 21 chapter three to discuss strategy with respect to collective bargaining ufc w afsc me If an open meeting may have a detrimental effect on the bargaining position of the public body and the chair so declares And I do declare with no intention of returning to open session Is there a second? Second stanzer second Uh, okay moved by mcdonald and seconded by stanzer. We are now in executive session. Oh, no, we have to vote. Sorry Um, mr. Menino Menino I Mr. Demling Demling I Ms. Dancer Stanzer I Ms. Spitzer Spitzer I Ms. Lord Lord I Mr. Harrington Harrington I Mr. Sullivan Sullivan I Ms. Seeger Seeger I And mcdonald I So we now in executive session


Before starting our discussion of hydrogen atom it is important that we prepare ourselves a little bit keeping that in mind today we are going to discuss different coordinate system from the Cartesian coordinate that is spherical polar coordinate and also we are going to talk a little bit about this rather important quantity that we must have studied in physics that is angular momentum. So, the question is why is it that we need to talk about spherical polar coordinate why must we work in spherical polar coordinates if we want to build a quantum mechanical description in angular momentum that is what we will learn in this lecture and why at all talk about angular momentum that will become clear when we start talking discussing our Schrodinger equation for hydrogen atom. So, spherical polar coordinates I hope are not completely new to most of us the same point in space that we conventionally described by coordinates x, y and z can also be described by r, theta and phi where r is the distance from the origin 000 point the angle theta is the angle between the z axis and the position vector you can call right position vector is a vector joining the origin to the point in question. So, the angle between z axis and that position vector is called theta and then if you drop a perpendicular on the xy plane let us say we drop a perpendicular on the xy plane then the arrow this blue arrow that we get this is called the projection actually it makes sense for me to join the two tips of the arrow. If you drop a perpendicular from the tip of this arrow to the xy plane then this arrow that we now get in the xy plane that is the projection of the position vector that we are talking with originally the angle between the x axis and the projection vector this is called phi it is almost hidden by the globe unfortunately so I will write again this is called phi. Range of r is from 0 to infinity remember r cannot go from minus infinity to plus infinity 0 to infinity theta goes from 0 to pi 180 degrees. You can ask why is it that does not go to 360 degrees because it is not necessary we are allowing one of the angles phi to go from 0 to 2 pi. So, the moment that happens there is no need for us to talk about theta more than 180 degrees that is why. So, of course I mean one can think that theta should range from 0 to 2 pi and phi should range from 0 to pi but this is the convention that is used everywhere we should not build our own convention unless it is absolutely necessary we go with whatever is the existing convention. So, remember range of theta is from 0 to pi range of phi is from 0 to 2 pi the relationships are very simple z equal to r cos theta quite simple right because if you draw a perpendicular from this point to the z axis something like this this is perpendicular what will be the length of the arrow on the z axis that is a z component that is z and what is this angle theta. So, it is not very difficult to see that z is equal to r cos theta r is missing here for some reason but here it is written r is the hypotenuse z is the side adjacent side. So, z is equal to r cos theta what is x all right. So, this length is r so and this angle is theta this angle is 90 degrees minus theta. So, I hope it is not very difficult to understand that the length of this arrow the projection that is r multiplied by sin theta r multiplied by cos of 90 degree minus theta that is r multiplied by sin theta. Now, when we look at this triangle here you drop a perpendicular from the tip of the arrow on the x y plane to the x axis is a perpendicular. Now, what we get is this here r sin theta this is your hypotenuse and this is the adjacent side. So, you get r sin theta cos phi. Similarly, y turns out to be r sin theta r sin theta is same in both because r sin theta is the length of the projection here r sin theta sin phi quite simple. You can work out the inverse relation here x y z the Cartesian coordinates are subjects of formula you can turn it around and make r theta and phi the subject of formula I will not do that you can do it yourself what we get is r equal to square root of x square plus y square plus z square that is of course very obvious right this is sort of the body diagonal r and the lengths of the three sides of the cuboid r x y and z. So, of course x square plus y square plus z square is r square or r equal to square root of x square plus y square plus z square what is theta actually what is theta comes from the first relationship anyway cos theta equal to z by r. So, theta of course is cos inverse z by r what is phi the easiest relationship is that what is sin phi by cos phi that will be y by x so that is tan phi is not it so phi equal to tan inverse y by x I said you do it I would not but then I ended up doing it because it is so simple anyway. So, these are the relationships and well I think by and large you can remember it but if required you can always derive it is not such a big deal the point I want to make is that spherical polar coordinates are things that we are sort of introduced to very early in our lives when we are in school if you think of a globe we have all studied geography at some level and we know about latitude and longitude what is latitude what is longitude are they related to theta and phi r of course is constant for the earth that is the surface of the earth but what about theta what about phi theta is not exactly latitude it is 90 degrees minus latitude because latitude remember is defined from the equator. So, what we call theta equal to 90 degrees in our system is written 0 degrees as far as latitude is concerned and there the range is plus 90 to minus 90 right. So, theta is related to latitude and phi is actually longitude phi goes around like this right in the equatorial plane. So, phi is exactly longitude. Now we have been already introduced to this d tau business we know that psi psi star d tau is the probability of finding the particle at some point r within a small volume element and we had said that if you work in Cartesian coordinates x, y, z then d tau is simply dx, dy, dz when we work in spherical polar coordinates it becomes a little different and this is something that we will use so we better learn. So, here the diagram is drawn already but I will still try to draw it so that we understand little better. So, let us let me draw here maybe so suppose I want to define a volume element at this point what do I do I increase all the coordinates a little. So, I can increase r by an amount dr of course the way I have drawn it this is a large amount actually dr is very very small compared to the length of r here I am exaggerating so that we see better all right. Next what do I have to do I have to work with theta how do I work with theta change theta a little bit so make it theta plus d theta. So, now I can draw another line where this small angle here where smaller than what it seems in this diagram is d theta.  So, two sides of the volume element are defined already one side is dr the other side is r d theta what about the third side how do I define the third side. So, drop this now I will increase phi a little bit like this. So, now our projection will go somewhere here now I can think of this arc this is the third side of the volume element just draw a perpendicular like this this arc is the volume element what will be the length remember this length here we already said is r sin theta and I have increased by increase the angle by d theta d phi. So, this is going to be r sin theta d phi I am not writing in a nice place this is going to be we will write here r sin theta d phi. So, the three sides of the volume element are defined now just to see whether we understand it or not I will draw the other sides of the arc as well let us hope I have not forgotten which color I used this is one and now I will draw r this is r again you have to increase this as well and just because I am a little bored of changing colors I will complete the volume element is the same color anyway. So, I hope you see the volume element here the volume element is not exactly a cuboid it has curved sides but the curved sides are almost linear because they are small segments of a large sphere you can think and in case you have had trouble understanding my poorly drawn diagram here you have a little better diagram here also you see the sides are dr r d theta and r sin theta d phi. So, the volume element volume of the volume element is going to be r square dr sin theta d theta d phi this is very important and we are going to use this later on in our discussion. Now, let us talk about angular momentum as you will see when we discuss hydrogen atom angular momentum is going to be a very important property that we will worry about. I think once again we all know that angular momentum is defined as a cross product of r and p r cross p what is the meaning of cross product r is a vector p is a vector l is also vector. So, l is the vector product of r and p what is the magnitude of l then magnitude of l is going to be r p sin theta and what will be the direction? Direction will be perpendicular if this to the plane of r and p r and p will always be in some plane. So, direction of l is going to be perpendicular to that. Now, let us work out what this is and while doing that it makes sense if you work with x y and z components to begin our discussion. So, we will write r like this i j k are the unit vectors along x y and z respectively and x y and z are the scalar values of well x y and z respectively. So, r vector is given by i vector multiplied by x plus j vector multiplied by y plus k vector multiplied by z and p vector is given by i vector multiplied by p x plus j vector multiplied by p y plus k vector multiplied by p z. We want to work out what is l equal to r cross p. And when we do that, this is what we get. First of all, why do we have 6 terms and not 9 terms? We should have got something like i cross i x square also. Well, the thing is we need to remember this i cross i j cross j k cross k everything is equal to 0. Because remember what the magnitude is going to be, it is going to be sin theta, i square sin theta that kind of thing would have happened. The angle between i and i, j and j and k and k, this angle is 0, sin theta is 0. So, cross product of the same vector with itself is 0. We do not have to worry about that. What about the others? i cross j is equal to k. Remember these are all perpendicular to each other. So, k is perpendicular to the, so k is basically along z axis, it is perpendicular to the xy plane. And j cross i is minus k that is important to understand. So, if you change the order in this vector product, the direction is going to change even though magnitude will remain the same. And it is very easy to remember also i cross j equal to k, j cross k equal to i, k cross i equal to j in alphabetical order, go in alphabetical order. If you are going in alphabetical order, you are going to get positive.  It is as simple as that. If you just want to remember it, of course, you can work it out and see what it is. So, let us see. In this expansion that we have performed, let us collect the terms in i. Remember i is obtained by taking cross product of j and k that is i and cross product of k and j is minus i. So, j and k, j cross k y p z, this becomes i y p z.  So, if I collect the terms in i, I get i multiplied by y p z minus z p y. This very nice symmetric expression and the other two terms also turn out to be like this plus j multiplied by z p x minus x p z plus k multiplied by x p y minus y p z. So, see what is y p z minus z p y? That is the x component of the angular momentum, because it is multiplying the unit vector along x direction. What is z p x minus x p z? It is the y component of angular momentum. And what is x p y minus y p x? That is the z component of angular momentum.  It is a very simple determinant form in which we can write this. So, this is the classical description. Now, let us think how we are going to write the same expressions in the language of quantum mechanics. Remember, in quantum mechanics, we have an operator for every physical observable. Operator for x, y and z are just position multiplying the wave function. Operator for something like p x would be h cross by i del del x. Operator for p y would be h cross i del del y. For p z, the operator is h cross by i del del z. So, all we have to do is in this determinant, we have to substitute x y and z by x hat y hat z hat respectively. And we have to substitute p x hat by h cross by i del del x and so on and so forth. When we do that, this is the angular momentum operator that we generate. If you know position and momentum operator, you can virtually generate all operators that we require. So, L hat operator is given by h cross by i multiplying this determinant i j k x y z del del x del del y del del z. This is what it is. Now, we will have something to say about the total angular momentum and z component of angular momentum starting from here. Basically, we want to write down the operators for total angular momentum and z component of angular momentum in terms of spherical polar coordinates. You will see why. The problem actually becomes simple. And why are you worrying only about z component? We will say that as well, even though it might be taking things a little too far for this particular course. So, in case you find that discussion to be too much, you can just skip that part. It depends on whatever is being done in your college. So, L x hat as we said earlier is y p z minus z p y L y hat will be z p x hat minus x p z L z hat will be x p y hat minus y p x hat. So, and then when we write the expressions for the p q hat kind of operators where q can be x or y or z, this is the expression that we get. Now, you know the relationship between r theta phi and x y z. Using these relationships, it is possible to convert from this del del z del del y to things like del del r del del phi del del theta. It is a little longish. So, we are not going to do it here. If you are interested, it is not difficult. It is just a little too long. You can do it yourself. So, it turns out that in spherical polar coordinates, L x hat operator is minus i h cross multiplied by minus sin phi del del theta, multiplying minus cot theta cos phi del del phi. You could also write h cross by i here instead of writing minus i h cross. For L y hat, the operator looks very, very similar. The only difference is wherever you have sin phi for L x, you have cos phi for L y. L z hat is the best of them all, minus i h cross or h cross by i, you can write minus i h cross or plus h cross by i multiplied by del del phi. Very, very convenient. That is what we are going to work with. And the other operator that is very important is not L. We generally do not work with L. We work with square of angular momentum. And that operator is obtained by taking L x square plus L y square plus L z square. And to cut a long story short, this is the form of the operator. This is something that will keep on coming back in our, in our discussion later on. Do you have to remember this for God's sake? No. We should provide this whenever it is required. There is no need to remember too much here. If you remember del del phi multiplied by h cross by i, I am very happy. L square, please do not try to remember. It will be provided in our discussions wherever required. So, these are the two operators that we are going to work with. L z hat and L square hat. Now, why is it that we are not interested in L x and L y? Because again, we are not going to do the derivation. If you are interested in the derivation, I recommend that you see my lectures that are available on YouTube for a more elaborate quantum chemistry course. You have to write Anindya Datta Quantum and search within YouTube, you will see 68 lectures and they are named. So, you go and see, go through the angular momentum lectures, you will get answers to whatever questions you might have at this point. For now, let us take it axiomatically that in quantum mechanics, if two operators commute, what is the meaning of commute? Meaning, you take a wave function, make a hat operate on it first and then make b hat operate on it. You get something. Then you reverse the sequence of operation, make b hat operate on it first and then make a hat operate on it. You get the same answer. So, another way of writing it would be this. What I am saying is you have some wave function phi. I will just write phi here, make a hat operate on it. You get something. Let us say a multiplied by phi. Now, make b hat operate on it. So, basically b hat is operating on a hat phi. So, this is what you get b hat operating on a phi. The other sequence, let b hat operate on phi, you get let us say b multiplied by phi. Now, let a hat operate on this b hat phi. This is a phi, sorry. Then you get a hat operating on b phi. It can be proved. We are not going to prove here that b hat a hat phi is equal to a hat b hat phi. Or you can write like this, a hat b hat minus b hat a hat phi equal to 0. That in the convenient notation that we write, we write like this. a hat, b hat within third bracket means a commutator, a hat b hat minus b hat a hat. b hat a hat, what is b hat a hat? b hat comma a hat, the sequence of operation is just opposite. Of course, in this case it will be same. But the crux of the matter is that if the commutator is 0, then they have a common set of functions. And properties associated with a hat and b hat can be determined simultaneously. It turns out again, we are not going to prove it here. It is there in those angular momentum lectures. It can be shown that L square hat and L z hat commute. That means, you can determine the square of total angular momentum and the z component of angular momentum simultaneously for a system. However, L x and L hat, L y hat and L z hat, L z hat and L x hat do not commute. They do not commute. So, L x and L y, L y and L z, L z and L x, they cannot be determined together. So, the only hope you have is to determine the total angular momentum and its component along one direction that we call z direction. Here, students usually have this question, what is z direction? I am talking about hydrogen atom, let us say. How does the atom know what is z? Atom does not know. Remember, wave function collapse? Remember that everything is, your system is in an entangled state before you make the measurement. Only when you make the measurement, wave function collapses into something. Suppose, I want to measure the z component of angular momentum. How do I see it experimentally? I apply a magnetic field, is not it? Zim and effect. So, the direction of the magnetic field becomes the z direction. What we are saying is, if we have an angular momentum, we have an angular momentum like this. When we apply a magnetic field, now this z direction is defined. So, theta is defined with respect to the direction of the magnetic field. Now, we can determine the length of this arrow, which is the angular momentum itself. Actually, we can determine square of it. We cannot really determine whether it is pointing up or down, just like just from here. L square is what we can determine. And the other thing that we can determine is a z component. So, from here you get L square, from here you get L z. Combining the two, you can say whether the arrow is pointing up or down of course. This is what we are going to discuss in a little more detail, when we talk about hydrogen atom.