Hey, great. Thanks, Todd. Welcome, everyone. Well, the first up is the action I interviewed. Todd, could you make it a little bit bigger so I can read it? Sorry. Thank you. Oops, that's too big. Oh, what happened? There we go. I think I can read it now. So the first action was for Chris and Mick to complete the read me blurb for the incubation, and I don't think I've seen that. Chris, I think you're on. I think you're on as well. So Chris and Mick, do you guys have an update on the... Hey, Chris, I'm just... I sent you the potential read me. Do you want me to just put it in as a PR on a high level? That's one way of doing it. Did you send me something? I didn't see it, or... There was a couple of paragraphs on the rewrite on the initial introduction. Okay. Could you just send it to the list? It may have been filtered out. I don't know. I'll have to look. I don't recall seeing it, though. I'll send it to the chat. Hello, this is Emmanuel from Accenture. Hi, Emmanuel. Welcome. Okay, so if you guys could send it to the list, that'd be great. What proposal is this? The next was for me to move the project lifecycle to the Wiki, and I didn't do it, but I know it did. So that one is done. And the same with the project proposal for the initial heavy age proposal that was moved to the Wiki. So those first three are done. The next one was for Dave to finalize the... I'm sorry. Is there a question? Yeah, I had sent to the TSC list. Yeah, so we met with Scott yesterday. It was fairly... Overall, we feel that Don's is strong. If you're not... He doesn't have mute on. I don't think he was as much of a mute on as Don was, somebody who was talking to Don is taking over the meeting. Turn on mute. I'm going to have to go ahead and mute everyone, and then please come off mute to talk. No, this is Chris Allen. I had sent a note to the list regarding the project lifecycle after some discussion. I met with Mick on Monday, and we're just talking about, in general, security software needs some additional stages, and I'm not sure that all the different stages that I put in my proposal are required, but I definitely feel like the experimental one is important. When you're doing a hackathon or things of that nature and want to share ideas, we need to have a category for that, which we don't, and then the evaluation stage that is basically an important intermediary stage where you can have it reviewed by cryptographers and security reviewers and security engineers and things of that nature, that just moving from, you know, into mature is too fast. So, you know, I wanted to, you know, I don't understand how the decisions are made as far as how the lifecycle document list is created. I've heard that, oh, this is the way that people do it, but this, I'm not really accepting that that's the way that people do it. So, anyhow, I posted the thing to my list. It was posted up for comments for weeks, but again, I think they're, you know, for whatever reason as far as, you know, how the processor hasn't really been an open discussion on it. So, I'm just, you know, I added it to my list of something I wanted to talk about. And if, you know, if nobody is interested in that evaluation, that's another story, but I think it's worthy of discussion. So, Chris, I mean, I think you were on the call when we approved this last week. So, I mean, we can have further discussion. One of the things that's on my list of things to do, and it should actually be in action, is to actually start the process of the TSC defining the exit criteria for an incubation, which is maybe what you're getting at. But it's, from my perspective, and I've been involved with quite a few open source initiatives that are running under open governance, and none of them go to this level of, you know, I don't even know what to call it, but I mean, incubation and then mature, and then, you know, wouldn't we call it? So, a lot of it I can throw out. It's the evaluation stage before mature. The, you know, it takes a lot of work to do a security review. It takes a lot of work to do the... That's not under debate, Chris. And I said that we're going to describe and define the process for the exit criteria. We will do that. But it doesn't seem to be that we have to actually change the life cycle itself in order to achieve that. So, if you've got specific criteria that should be addressed, let's start discussing that. Absolutely. Absolutely. But that doesn't change the process of going from incubation to mature. If you're saying that it's a very high bar, that's fine. We can have that discussion. But I don't think we need to have, you know, all these little fine-grained levels of, you know, between incubation and mature to describe... I don't see what value that adds. Again, I will accomplish some of these initiatives, and they all have incubation, they have mature, and they have deprecated or attic or other various terms that they use for the stuff that they're no longer using. So, if I can just... Is the concern... This is a question for Chris Allen. Chris, is the concern about the labels or about the criteria used to advance from stage to stage? It's a little bit of both, because it communicates things to the community that, you know, where sort of the intent is. The, you know, one of the things about incubation is that, you know, we're going to potentially have five, six different things that are going to be incubated. But we, on the other hand, we want... We have a goal of, you know, trying to bring things, choosing one for a single code base.  And that's a signal and a process point that, you know, exists before production. And that's the... I mean, I put in a longer list, and I probably should not have, but the key one is that particular phase. It's something we're still careful with maturity. If you go back to view the minutes of the technical steering committee meetings, you'll see that one of the points that we agreed to do was to start focusing on exactly what the exit criteria was. And so, in the context of that discussion, Chris, this is, you know, we can certainly add in all the things that you're talking about as a function of the exit criteria from incubation to mature. But I don't think that it necessarily abrogates exactly what was in the lifecycle proposal in the first place. There's just... The pages are pretty clear. Everybody, you know, pretty much understands what these things mean. And I think we should move on. So, I mean, you know, what we can do is we can set up a small subgroup that starts focusing on the exit criteria. And you're more than welcome to participate in that, as is anybody. And, Chris, can I have a moment? Yep. There's some confusion. Several people have talked to me. Just to be really clear here, this is going to sound mildly repetitive, but this is an open-source project, right? There were five weeks of discussion around this topic. Everybody's welcome to participate. People did participate. If you don't feel like you can, you can. It's an open-source project. And so, you know, saying things like there's no open discussion, if you haven't had five weeks of open discussion, it's a community. And so, you have to, you the participants, you know, I'm from the Linux Foundation, I sit down on a lot of the projects, you the participants have to participate, and participating ex post facto doesn't help. So, if the discussion's going on, you have to be engaged in that discussion while it's going on. And once decisions are made, you have to move on. Coming back and bringing it up, it's not like anybody's excluded from those discussions. Everybody's invited in. There's 100 people on the call. And all 100 are welcome to comment. So, I just, I think there's a bit of an understanding, or lack of understanding here, that the TSC call is the discussion. And when the discussion's over, the discussion's over because the TSC has made a decision. Right, well, but the discussion can happen in Slack and on the mailing list. Yeah, yeah, absolutely, yeah. It's all part of that whole community. Right. So, let's move on with, you know, just wrap up the action item review, because I'd like to get to the Intel proposal. So, quickly, so Dave was going to finalize the wording on the white paper. Obviously, that means Dave and the working group, but, and get in front of the board to review. I take it that since the white paper's not finished, this hasn't been done, that's fine. Yeah. Yeah, so Chris, we, I think we were specifically talking about the section of the white paper that made reference to a permission versus a permissionless type. And we did, we did update that section. So, what we're planning to do, and I can cover this when we get, when we get to the working group update, but basically, you know, we're going to have our first draft, draft 01 or whatever, published next, next Wednesday. And then I think what we'd like to do is show that first draft and then specifically highlight that one section, because that's just the one, what we were talking about last week was just kind of, we wanted to zoom in there and just make sure that they're comfortable with how we're describing a non-permission use case as well. That's the point. All right. Thank you for the clarification. Todd, if you wouldn't mind just clarifying that, that action item and we'll track it. We'll do. And then I take it you updated the, did you update the minutes for the work group? Yep. Yep. So I was able to follow Patrick's format. And so now if you click on the white paper working group, you'll see a member section and then, you know, an entry for each week, each weekly meeting minutes. And that's in there. Okay. Thank you. Excellent. So we can close that one. Chris Allen, Chris Rowan rather, Canvas everybody interested in the identity subgroup and find out if they want to list or just use Slack. Chris will we be able to close on that? That's, we're having the meeting on Friday at 2 p.m. Eastern, 11 p.m., 11 a.m. And that is the first agenda item for the meeting. There are 14 people that have said that they want to participate in that discussion. Excellent. Also part of it is that we're not absolutely sure, you know, should this be a separate group or whatever. So, you know, this is just, you know, a first meeting to sort of Canvas what it is that, you know, why people are interested in the topic and what we want to try to do. It could be that it, you know, we instead roll into architecture or requirements. It just was a unique area. Okay. Great. So we'll just track this one, but thanks. And it sounds like there's a lot of good parts on the identity group. Todd, you want to update us? Whoops, just lost the agenda. You want to just update us on the two doodle polls and thinking about the tooling face-to-face and the next technical face-to-face? Yep. Sure thing. So in terms of the technical face-to-face, there have been about 20 people that have responded. The most likely date is looking like that Thursday and Friday after the consensus conference in New York. Though the following week looks really strong as well. I would like to see a few more people respond to the doodle poll. So we'll leave this open for about another day or so. So the people on this call and the people that see the TSC minutes have a chance to respond. And then we'll close on it from that point. But along those lines, if anyone in New York City or, you know, in the East Coast have space that they would be willing to offer up for this to hold the face-to-face, definitely get in touch with us and we'll be reaching out as well. And then on the other topic for the tooling face-to-face, only a couple people have responded at this point. Five people have responded. And three of those people are not available at any of the times that were proposed. So I suspect we're going to either need to look for a different time frame. Yeah, maybe we're starting to sort of run the calendar here. Maybe the things, although I did want to be able to sort of start this, maybe we just don't need a face-to-face and we just have to have a two, three hour call to sort through the various tooling needs. I started to put together a little bit of a list. I need to focus a little bit more on that maybe later today. And I can't remember what I was doing. I'll have to go back and look where I was doing that, whether it was a wiki or maybe it was just a slack. And have other people sort of chime in with some thoughts. But if a face-to-face is not in the cards, that's probably fine. It saves a little bit of budget for travel and so forth and we can just have a two to three hour call in the next week or so. All right, that sounds good. Yeah, so why don't I work with you and Steven and see if we can't figure out a time for a call and get that out to the list and anybody can dial in if they like. So I'm actually going to follow up with you and Steve. And Chris, to that end, there's a page on the wiki that I'm logging all of the meetings on. It's Hyperledger, Hyperledger wiki. And down in the bottom you'll see a list of a calendar link. If I've missed any on here, just send them over to me in Slack or wherever else. I have the recurring meetings, the working group meetings, and the meeting proposals up there right now, including the doodle links. And as they become meetings, I'll post them up here and this should be a good way to get them out and easily in hand. Excellent, thank you. This is Ram. It looks like I dialed in just around the time when you were talking about the word group updates. I just wanted to mention that, you know, we are meeting the architecture word group. About nine, 10 people were interested and about six, seven people have confirmed that they will be able to attend tomorrow based on the doodle poll. Okay, that's a little premature. We're just actually just going through the action items, but that's... Thank you. Thank you, Ram. Oh, you're going through the action item, sorry. Yeah, you're just clicking at the action items, right? And Phillip was just telling how he had created a calendar. I think Chris Rowland had suggested a calendar. I think it was a great idea, so Phillip just followed through with that. He was just identifying that he's posted the meeting times and so forth. So, any proposed or meetings that aren't listed in the calendar, please get with Phillip and he'll add them. Okay. Okay, so I think next up on the agenda, I lost my, here we go, is the proposal from Intel. And is there a link to it? I'm sorry, before we get into it, can I ask you a question? Can I ask a question of Chris Fennix? This is Jatinder Bali from Citigroup. Go ahead, I'm here. Yeah, so if there are... I just want to get your answer. If there are more than one very strong proposal for a hyperledger, are you considering, just like we have different versions of flavors of Linux, are you considering having two different fabrics, or would you not accept that and just say one has to be the best of both worlds and only one fabric would be accepted? So, let me see if I can address this. So, I think it's a good question. Thank you. And the answer is I don't really know. I think, again, as Phillip said, this is really a community. We have to, this is something that we as a community have to decide. This is not up to me or anybody, any individual. It's not to the board. It's up to collectively the TSC, ultimately, to make this decision. But here's my take. Here's what I'm thinking. And again, I don't want to take away, I think this proposal is fine, but I'm, you know, I would like to see that, you know, this group come out with a thing and a thing that can be used in multiple flavors, right? So, you know, we talked about the scope initially and how we were focusing on, you know, the very lowest layer, the sort of the core, not on building out a specific framework for banking or supply chain or anything else. And that from that core, you know, the analog of the Linux kernel that you could have multiple things, multiple flavors, multiple platforms that may compete or not, or that may be, you know, different domains and so forth. That's what I would personally, me personally. This is not me or it's not IBM. It's not the TSC. This is just me personally. It's not the TSC as drive towards an answer that, you know, the world can use. I know others, you know, think that there will be many blockchains and I think that's true. But I also think that at the core, there really don't necessarily need to be multiple, you know, entity managers and multiple, you know, databases and multiple, there may be different consensus modules, but I would hope that we could have a framework that could allow for pluggable consensus. And then, you know, that we don't necessarily need to have multiple approaches for how we deal with smart contracts, but we may have different smart contract languages, like we may have Hopper and we may have, you know, I don't know, the security or, you know, the go, you know, version that was contributed from IBM initially and so forth. I would hope that we had a number of different approaches for that, but those are just core pieces and that you can then assemble those core pieces, which we would, you know, strive to harden and so forth, just like they've done with the Linux kernel, but that would leave room for a market and a whole ecosystem of opportunity that was built from that kernel. So that's my personal vision. You know, we're going to discuss the Intel proposal and, you know, as we discussed in the past, we can have multiple proposals. And I don't necessarily, you know, I would hope that as we consider this proposal and potentially approve it that we also are starting to think about, I think what is hinted at in this proposal is how we can take some of the great ideas from all the different incubation proposals that we may or may not see and come out with something that we can all, you know, that we've collaborated on together and that we think addresses the, you know, the set of use cases and requirements that the requirements team is working on and so forth. Does that make sense? Yes, yes, definitely it makes sense, right? When I wake up on Monday morning, I love the Intel proposal. Tuesday I go back on IPM proposal, I love that one. It's, I mean, there are so many things in both and many other, I mean, many other legions, right, that we need at least, you know, your answer was great, right? If it has got these modules and then we can plug in previous modules, that would be fantastic. Yes, thank you. But, you know, so let's turn this over to Mick and Patrick to present and let's have a healthy discussion. So Mick, Patrick? Okay, thank you. This is Patrick Holmes from Intel. Can you see the screen? Okay. Yep, thank you.  I'm just displaying this, the same document that the link was to. Again, Patrick Holmes, Intel. This is a hyper ledger improvement proposal. It is co-sponsored by Mick Bowman at Intel Corporation and Richard Gindle Brown at R3. And the content came from both. I'm not going to read this word for word. I assume that's okay. I'll just walk through it. So, the abstract. So, the proposal is to accept the Intel distributed ledger into incubation. Incubation status and we're proposing the name Sawtooth Lake. And then collaborate with others to improve the project. Then formally evaluate it as one of the foundational platforms under the hyper ledger umbrella. The motivation is, well, first we think it has some compelling features. Most notable is that we've decoupled the ledger from the transactions. The second is the concept of transaction families. So, we have very extensible, very pluggable with different data models and transaction semantics. So, very extensible. And then we've also got the pluggable consensus which enables different consensus protocols. Which would support both permissioned and non-permission networks. So, we believe these are compelling features. They make it worthy of consideration. Eventual evaluation once we have an evaluation criteria. And we think having multiple code bases facilitates a deeper discussion of the requirements and vision. And we can explore and test different ones, different assumptions that underpin each of these designs. The members, the observers, the users could develop a better understanding of the problems at each approach. And maybe come up with some shared requirements. But there are also improvements to be made to all of the code bases. And while we figure out the use cases, the requirements, the evaluation criteria, we'd like to collaborate with others. Smart, passionate developers from both the hyper ledger companies and the public as best way to improve the software. So today we're proposing that this move into incubation status. We have several tasks in mind that we'd like to collaborate on. And I've listed several here. We need to continue to develop the artifacts, develop tutorials for developing transaction families, develop some transaction families, extend our endpoint registry transaction families to work with permission services, identity, authentication and permissions. Permission granularity from permission nodes right now, they're not permission, but they could be extended. Develop a blockchain explorer, a network explorer, etc. The effort depends on many factors, so I can't tell you I didn't size the effort to do all these things. It really depends on the community involvement. Intel is committing several full-time engineering resources to ensure the success. The initial maintainers would be myself and Sean Amonson at Intel. We are open to having other maintainers once they've made some significant contributions and demonstrated a good understanding of the code. Other Hyperledger project members have indicated to us they're evaluating the code and they've expressed interest. Now the how-to can change, but the idea is that we'd create a single repository within the Hyperledger organization named Sawtooth Lake. That repo would point out to another GitHub organization such as Sawtooth Lake, which would hold multiple repositories containing the project. We think that's a better approach than trying to combine all of the repositories into a single one. We also don't want to take more than one in the Hyperledger organization. In terms of closure, we'd work to continue on this project until it graduates to a mature status or we make some other decision. By that time, we think there'd be a more robust system for prioritizing managing improvement requests. That is the proposal. Thanks, Patrick. Any comments, thoughts, questions for Mick or Patrick? Richard here, is there a comment for me as a co-sponsor of this? Just to echo some of what Mick said, I was particularly pleased to see this contribution because it ties, I think, directly to a point that I and others have made that there are many architectures we should be exploring and this allows us to do it within, if the innovation is approved, allows us to do it in the context of the foundation. In particular, looking at some of the codes from the design docs, my sense is the Intel approach makes them as well as having a different design. It makes them very different assumptions about the problems it's trying to solve and how it might be used. I figured that could be quite a useful way to help us as a group get to a much clearer idea of what problem or problems we're trying to solve. So I hope this is one of many new proposals for incubation. Hey, Chris, this is Morali from DDCC. So this is a question for Patrick. So I saw several things being mentioned there in terms of data explorer and block explorer and other things. I just want to confirm. I think wouldn't the first step be as to how to integrate the Intel platform with the OPC or the other code bases? How does this interface with the other two things that we have? That would be the first step, correct? Not necessarily. I think it would be a mistake to rush to try and integrate as many different solutions as possible. I think we could wind up with a Frankenstein of a system. There are different languages, different architectures. I think it would be best to understand the different approaches, the different architectural approaches, the pros and cons of each, and do that first. As well as continue developing the requirements, the architecture, the white paper. So we understand what it is we're looking for. Okay, because I was going based off Chris' comment that we want to develop this common framework or fabric which will allow that plugability that other things could be added. So you're saying this will just independently evaluate first and then think about it later. So let me try a slightly different version of this, which is the OPC code base takes a very, starts from a kind of permissioned PBFT based consensus kind of model and then is trying to move towards other usages. The Intel chain starts from a more open permissionless model and is moving towards the permissioned spaces. And I think the two architectures will at worst inform us about what the potential design space is for the final solution, whatever that is. And if there are fundamental differences between the two of them, that's also useful to know because that identifies a couple of different optimization points. We don't have one database. We have structured database and the non-structured database are SQL and no SQL database because they serve different purposes. We try to make them as common as possible and try to build libraries that allow us to move back and forth between them, but they are different optimization points. So I second Chris on the ideal is to come out with a single set of building blocks that can be used to put together. I think the process in getting there and in particular having a plurality of approaches allows us to bring thinking from different sides to this problem as we sort of figure out what those components are. You know, I will say personally, I don't think there needs to be just one identity service. I think that identity is one of those things that we have historically found to be decentralized. This will give us an opportunity to actually do some exploration into those kinds of assertions about what works and what doesn't work. Thanks, Mick. So other questions, I was just trying to chase the chat, but it seems like this user interface doesn't like me to go back far enough because as soon as somebody types it, it tells me what the latest thing was. Chris, there was one question in case everybody's not following the chat. I forget who it was who asked. Somebody asked me, Richard here, how sort of the incremental and quarter of three were late? Are they the same thing? What's the relationship? The point I clarified in the chat is that they are separate and different, and in particular they make quite different assumptions. I think about the problem spaces to which they'll be put and the design that's needed as a result. And it's actually precisely for that reason that I was so keen to sponsor it because it does come from a very different way of thinking in a different problem space. So it adds to the range of options and then the range of thinking from which we can all draw and learn. So just to clarify, quarter, which we announced last week and is still under development, is separate. And as that matures a bit further, it's at that point where we will be releasing the source, but hopefully that clears that up. Okay. Thanks, Richard. So let me just ask generally the community here. You know, as I mentioned, and I think as you alluded, these environments can inform one another, and I hope they do. The question that I have, though, is how does that happen? And how shall we, as a community, how shall this TSC sort of set things up so that we are encouraging, you know, the sawtooth-like chocolate to get into the fabric, peanut butter, whatever. I mean, this is my concern and my fear is that if we, and again, I'm not saying that I don't support this. I do support, I'm fairly supportive of this notion, but I'm concerned that if we go off and develop sawtooth-like independent of the fabric proposal, that we approved the previous week, or two weeks ago I should say, that they become independent things with, and there's not a whole lot of cross-pollination. That's a little bit of what I'm concerned about, and I'd like to have, you know, I'd like to figure out how we can, you know, work towards getting some of that informed cross-pollinations and getting towards a process for how do we take these forward, whether we work them in parallel. So, Chris Allen, I'm really looking forward to doing exactly what you're talking about.  And, you know, they're Tendermint, which is another group that has, you know, had some ideas in that space, but we weren't quite comfortable completely with that, and I thought Intel did a good job in that area.   So I'm hoping that there will be more, a few more incubations, and I'm very happy with the Sawtooth Lake proposal. Yeah, so again, thank you for that, Christopher. You know, and again, I agree very much that there's much that we can each learn from one another. And again, what I'm looking for more is a sort of thought process on how we make that happen. Maybe we look at the next hackathon and, you know, and we basically do a bit of musical chairs or something and, you know, have the LBC guys hacking on the Sawtooth Lake and vice versa. I don't know, I'm just sort of throwing that out. But I mean, I think we need to, I think collectively as a group, we need to figure out how we turn this into something that is collaborative and engaging as opposed to turning it into a bake-off, because I don't think a bake-off is a healthy situation. Chris, I think it's very good. Go ahead. Hi, Chris. This is Ram. I think, first of all, I think having a diverse set of solutions being brought here is, I think, a very good thing for the long-term success of this effort. And so, you know, I'm glad to see the internal contribution and especially the kind of different approach that they have taken. So with regard to, you know, the overall approach, you know, one of the reasons I've been kind of saying that, you know, discussions around the use cases, requirements leading up to, you know, a healthy debate on the architectural options in the architecture workgroup is that, you know, it gives us a forum, if you will, to have somewhat of a top-down approach, which we can then say, hey, you know, from the bottom up, the contributions, how can we evolve to a more, at least a unified framework, if you will? And I think it's very desirable to have as much of a unified framework as we can achieve and if we can use, you know, that kind of top-down discussion to say, hey, what are the pros and cons of the different approaches? What are the, if you will, if you have to divide the solution space into kind of different options, how do we want to kind of do that in a somewhat unified and thoughtful way? So I'm viewing that approach as the way where we can use those, you know, those discussions to come up with a unified framework. Now, whether we will end up with one ideal architecture, you know, that's an aspirational goal as far as I'm concerned, but I think we ought to try for it. Hi, this is Dave. So, you know, I could definitely envision over the course of the next six months, six or seven or eight new blockchain fabrics being proposed to come under the Linux Foundation Hyperledger project umbrella. And are we going to, I mean, this isn't specific to, you know, mixed proposal, which, again, I read through it, it looks great, like it a lot, but are we going to let every single proposal come in and live there, or is there going to be some kind of criteria that we're going to use to assess which ones we do want and which ones we won't?  And I guess the risk there is, maybe this isn't a risk at all, but maybe, especially if our attention gets spread out across lots of different things and, you know, we may not make enough progress on any one of them, or maybe it's a situation where, yeah, let's go ahead, let's them all come in and then we'll just see which one gets the larger development community and moves forward the fastest. But, you know, like I said, I think there's lots of potential future fabrics that I think are going to be proposed. I think if I was building a brand new blockchain, I would like, and I wanted to see it open source, I'd like it to be under the Linux Foundation and this as well. So, you know, we should be thinking ahead and deciding, you know, if we're going to make these evaluations, which ones we actually do want to incubate because of, you know, the timing and everything, you know. At what point do we say, okay, we've seen enough, we've considered enough, and maybe it's driven out of use cases and requirements, but, you know, I think there's going to be more coming. So, Dave, if I can just, you know, I think the earlier discussion went to what we were talking about, which is the kind of exit criteria. Do we put the filter on projects that are coming into incubation, or do we work hard on identifying what the set of exit criteria is for what comes out? Foster ideas, and it does change a little bit of our notion of what incubation and mature is. But I will agree completely with you that, you know, one of the things that does point out is that we don't have a sufficiently mature set of requirements or other criteria that help us kind of filter through these things. So, I agree. Hey, this is Morali from DDCC. I think, like, this is my opinion, I think we should all aim for a common fabric, you know, like Chris said, if everybody starts proposing, then we're all bifurcated, our resources will all be distributed. If we all work towards a common fabric, and the common fabric could be, you know, we can take much of it from Intel, or if you have to break down the components within the OBC or DH or whatever it is, right? But I think the aim should be developing this common fabric. Again, this is, you know, this is my opinion. Thanks, Morali. Other thoughts, comments? There's more chat. Kind of increasingly hard to track. This is Chris. I mean, I think this is sort of the root of why, you know, there were some questions in the last two calls regarding the, you know, the initial incubation, which is we didn't have that, you know, enough requirements and architecture things that some of us were uncomfortable with the incubation status because we felt like, gosh, that means, thus, that means that has to be the base fabric. And we were basically told, no, it isn't the, you know, necessarily the base fabric, and that there will be multiple incubations. And now we're kind of, you know, coming back and going, well, no, well, we want to have a single fabric and thus those things that are incubation have to be, you know, have to be already in it. And I still come back to, I mean, whether or not it's through the lifecycle or not, it's feeling like we're missing a couple of stages, which was kind of my opening argument in the beginning, that there is an evaluation stage that is, you know, missing here either before going to incubation or out of incubation into, you know, to mature. So, I don't know. Yeah, I think this is Sharon from IBM, you know, Ben's not on the phone today, but I do agree that we need to have a common fabric. And I believe pretty strongly, as I know, you know, the rest of my constituents here agree, we need to bring in the best pieces. And there's a lot of innovation in the industry, right, and we should bring these pieces together. So I want to make sure that whatever we do, right, we're looking at all the pieces coming in, bringing the best to the best and the best innovations together. But I also agree, we've got to make sure we get the requirements down so we're all headed to the right goal. And this is Morali from DDCC. And maybe Intel proposing this is that opportunity, right, of identifying, you know, what is the fabric from the Intel side, you know, what is the fabric from the OBC, what is the fabric that DAH has, right? And what are those? Can we pick and choose the best elements? Can they interoperate, right? Maybe this is the opportunity for us, you know, this hip will allow us to do that, go through that process. Yeah. And it's almost like this is why I really liked the face-to-face that we had, the hackathon, because I felt like, we're bad, the DAH pieces and the IBM pieces started to come together where we're trying to bring the pieces together. And then maybe we need to do that here. What pieces do we need to pull together from the two proposals together to figure out what's the best of the best and how do we move forward, right? And then from the third proposal that comes forward, same thing, right? This is Mark here. I agree with this 100%. I'm a big fan of sort of the modular architecture and plug-and-play and extensibility.  We just need to have some way of dealing with fragmentation and some way to try to streamline things so that we avoid sort of one-tenth of the people working on, you know, 10 different proposals. Hey, Chris, you know, this is Morali. You know, I can volunteer to, again, pull this team from Intel and IBM and DAH, right? To understand the fabric across all the three and, you know, see if there is something, you know, before getting into the code level, understand the architectures of each of those fabrics and see, you know, how things can work together, right? If that makes sense for the rest of the group. So if I can just jump in here. One of the things that I think is already starting to happen in the working groups that I'm participating in is that the different approaches are leading to some really nice generalizations. So at least in the white paper group, and I know in some of the discussions leading up to the architecture group, we'll see how that proceeds. And certainly from what I'm seeing built out in the requirements, use case groups. So I think, was it Sharon that was talking earlier? Again, I think that is our ultimate goal is to identify those pieces and to move there as quickly as possible. I think it's also useful for us to encourage a couple of different viewpoints that bring and apply tension to the architectural decisions that we've made to help us understand the spectrum of what those building blocks need to be. That is, you know, having one code base means that we come up with a really nice set of blocks which solves that one problem. So I think Mike was saying in the chat earlier just about the filter can be not at the incubation, but as it comes out of incubation and among the, I think, set of criteria are breadth of adoption, breadth of use, generality, appropriateness, all of those kind of criteria of what constitutes the best building blocks. Thanks, Mick. You know, I tend to agree very much. And, you know, I think that, you know, it's our job to figure out how to encourage that, right, encourage that output. You know, the thing that I'm very encouraged by is that, you know, this discussion is all about that. That makes me happy because, but again, I think, you know, the devil's in the details as they say, right? So here's what I would suggest. Let's take a vote on this, unless Mick, you guys want to let people think about this for a week or so. But if you're interested in having and calling for a vote, I could certainly start that process. But then let's, you know, let's take the next step of formally pulling together, you know, the group that we talked about doing. And, oh, is it hard to hear me? Can you hear? I can hear you, Chris. Let's pull together the group that's going to sort of noodle on the whole exit criteria perspective. And then, you know, let's also start thinking and discussing in Slack and the mailing list about just how, you know, different ideas about how we can sort of work to encourage the cross-team collaboration that I think is going to be necessary to achieve what we've been discussing this morning. Again, I'm very encouraged, but again, the devil's always in the details. And I guess I would like to call for a vote if we're in a situation to do that. And again, I don't see the incubation projects necessarily being bound to an answer to how we get to the end. I think the takeaway, and in many ways what I like about the fact that we have two, is that it's forcing us to start answering some of these questions about how we get there and what those criteria are. So, yeah. I agree. So, Nick's calling for a vote. Can I get a second? Sorry, I was on mute here. I was taking that. So, I do want to call you all. Sure thing. I'll just walk through quickly. Can I get a second manual? I'm on mute if you're on mute. I think Todd muted everybody at one point this morning. Come back to manual. Stan? Tomas? Yes. Stefan? Stefan, you may need to come off mute. Come back to Stefan in a second. Parda? Yes. And Chris? And Dave? Dave? You know, I'll say yes, but I think at some point we do need to draw a line in the sand and talk about how we're going to approach the next ones that are going to be proposed. And then just going back quickly, Stefan? Just going back quickly, Stefan. Yes. All right. And then lastly, Emmanuel on the line still. All right, Chris, that was nine of the 10 that were on the call at the start. I think we may have lost Emmanuel at some point. Okay. All right. So we have an approval. Thanks, everyone. Thank you. So I guess the action for Patrick and to me to start the discussion, I think, would people be interested in having an off cycle call? Well, an ad hoc call to talk about the exit and potentially entrance criteria, as David was suggesting. Isn't to a certain extent that's what the requirements group, which is meeting on Monday, an architecture group, which is meeting tomorrow, kind of beginning to establish? I think the requirements are an aspect of the criteria. I don't think they're exclusive. I think there are other things like, you know, many organizations, many open source projects require, you know, take Apache, for instance, so you have to demonstrate a diversity of contribution and participation, collaboration in order to exit incubation. So it can't just be a single vendor thing. And I think there are going to be other aspects, you know, the sort of the non-functionals that are going to be applied as well. And so, again, I think there's a broad set of things that we need to consider as part of this process. And I don't think it'll be all articulated in requirements. Again, this isn't waterfall, but I do. So I agree with you. I'm also concerned about the number of meetings.  You know, we could wait until next week, but that doesn't get us moving the ball. I'd like to move the ball. I'm going to have the discussion in Slack or mailing, you know, on the mailing list and try and get some of that out of the way. You know, that's an option before us. I'm asking basically if people are interested in having an ad hoc call early next week to start discussing some of this and start working on building a formal proposal in deafening silence. Does that mean nobody wants to do that? I think it's a good idea, Chris. You know, I'm just, myself, my calendar is just book solid next week. And I just don't have time personally, but I agree with you that it should happen. Then why don't we do this? Why don't we take it to Slack and start the discussion there and see if we can, you know, start work on maybe a Google Doc or something that starts to form our thoughts around that. All right. Try it that way. Okay. Thanks, Patrick. And as I mentioned, Todd, so Patrick has an action to get the repo and I have an action to start the discussion on the criteria. Next up is the workgroup readouts status updates. Patrick, you're up again. I'm up again. Okay. The requirements team meetings are going to be held every Monday from 8 to 9 Pacific time. The details, the meeting details will be announced today on every possible channel I can think of, so there's no confusion. There was no meeting this week while we were polling for the preferred daytime. Obviously, we could have had one. I apologize for that. We do have an agenda for Monday's meeting, which I discussed last time. Primrose from Accenture is going to go through the counterfeit drug use case. The progress is we discussed last week we're going to do top-down user stories, but we also thought we should do bottom-up and we now have an outline for our requirements document. It's just a start, but at least we've got something. And so we'll go from there. Okay. Thank you. Ron, you gave an update earlier, but you want to maybe just quickly repeat what you said earlier so that everybody who may not have been on at the time gets a... Ron, you may be on mute, or he may have had to leave. I think he had to leave. Sorry, I'm here. It's the mute. The multiple mutes. Yes. Just to recap what I said earlier, the architecture workgroup is going to meet tomorrow at 10 a.m. Pacific. I think I've sent the WebEx to the folks directly who responded as well as on Slack and on the email list. Please do join if you're interested. Initial meeting is just to go through the framework in terms of what communication channels we want to use, how frequently we want to meet, what are the tools we want to use, and also kind of get people's input on the work plan. Should we wait for the requirement workgroups to kind of be at least ready with their first set of requirements, or should we plunge ahead with the well-known architectural choices in front of us so forth? So looking forward to getting started this week. Great. Thank you, Ron. And Dave? Hi, yes. So as I mentioned, we have our minutes posted up on the Wiki. We met yesterday. We're meeting it weekly on Wednesdays, 1 p.m. Eastern Standard Time. And we had a full attendance. Everyone attended, and then they're right smack on time. Thanks, everyone. We kind of kicked off meeting reviewing the Wiki page structure, going over our prior minutes. We discussed the process that we would like people to follow for how we want to solicit feedback for the white paper. And basically every two weeks, we're going to be generating a PDF from our Google Docs working draft and putting that on the Wiki, and then alongside of that is going to be a form that we're going to ask people to that would like to provide feedback on the draft to kind of fill in there. It's a template for providing feedback and then that would be emailed to the working group members. And then we would be reviewing them and incorporating it into the next draft. So every two weeks, we're going to be posting a PDF alongside and reviewing people's feedback. And then we just started stepping through, going through the various revision proposals that the team had been made. And at the end, we just kind of talked about the process. Are we comfortable with it? We noted that it is going to take some time, but that's probably okay. In order to get everyone a chance to provide their suggestions and have enough discussion around it to actually update, it's going to take a little bit of time. But the fact that we already are incubating now two projects, it's not going to be holding back anyone. And also it would be good to be able to, to the extent that as we're making progress on the requirements and working in use case groups and things like that, and since members of our working group are also participating in there, we'll be able to get some of that feedback coming through those channels as well. And that's about it. Okay. Thanks, Dave. And Christopher. Yes, so immediately following the initial architecture meeting is a, let's call it a box for right now around identity. There are a lot of issues in the identity area that may or may not fit neatly into requirements or architecture. And we want to try to have a further discussion about specific around things like token hardware, different forms of authentication and authorization, privacy issues, selective disclosure, and other different things that are very specific to a number of the use cases that maybe are not the two, you know, the specific architecture requirements.  We'll decide at that point whether or not we want to formally make it a working group and have further meetings at that time. Okay. Thank you. And last actually, we should be the continuous integration group. I haven't done anything there because the first thing we need to do is have this meeting with Steven and the Lynx Foundation infrastructure team to get the base tooling up and running the Garrett and figure out if it's Travis or Jenkins and so forth. So we have, I have an action to try and get that on the calendar for early next week. And I will do that. But I did have overwhelming response to that. So now that we have two projects, that's actually a good thing. But they're an awful lot. And so thank you for all of those of you who did sign up for the CI work. It sounds like we'll have lots of help with that. So that's a good thing. And that's really it. Unless anybody has anything else for the agenda, we can all get about 15 minutes back. If we're hearing no other agenda items than Todd, I think we're adjourned. Thanks everyone.


Shall we begin? Let's. All right. So, yeah, it's not today. It's Tuesday. Tuesday. We have the next slide. All right. So, we are talking about the simple harmonic oscillator. And as we discussed, it's one of the most important problems in physics, and so it's quite important that we focus on it in quite a bit here. And so the first thing that we did the last time and I wanted to review and emphasize the important points is just to look at the classical mechanics of the simple harmonic oscillator written in this particular location with particular emphasis on some of the particular features. So, the first thing we did is that we wrote everything in terms of dimensionless variables. That's always what you should do. So you should always get rid of the units by looking at whatever the characteristic scales are and whatever the problem is. It has some physical constants. In this case, there's two constants, the mass and the spring constant or the mass and the resonance frequency. And that's it. So everything is kind of defined in terms of fact. And at least that relates whatever characteristic units we have will be defined in terms of those physical constants. So there's some characteristic energy, there's a characteristic height scale, there's a characteristic momentum. And by this, we have, you know, they're loosely related in this way. I mean, the Oprah, that we put a factor of two in there or not, that doesn't matter. That's because, of course, everything would be rescaled in terms of that. And I keep oscillating my simple harmonically. I'm oscillating. It's inside whether I want to put that factor of two in there or not because there's nothing solution. I think I just used a factor of two somewhere. Anyway, with that, the Hamiltonian looks like this. It's symmetric. It's quadratic in position momentum. It would be symmetric. And I would say whether this factor of two is absorbed here or put there, your choice. But we'll use this. So in dimensionless units, then, the Hamilton's equation of motion for the space-space variables have this kind of symmetric form. And each one of those, the canonical variables, the position momentum satisfy the simple harmonic oscillator differential equation whose solution I've written here in terms of initial conditions, the initial condition for the position in the momentum, or I can think about it as the initial amplitude and the initial phase of the oscillator. So one important point here that I want to emphasize is that any simple harmonic motion, any simple harmonic motion that's oscillating at a fixed frequency omega can always be thought of as some amount of cosine and some amount of sine. Always. And those are sometimes called the quadratures of the oscillation because they are 90 degrees at a phase one another, so they are said to be in quadrature. So let's say I'd like to go engineering and radio jargon, radio, whatever, but that's what we talk about. We still talk about the quadratures of the oscillator. Or I could equivalently think about any harmonic motion always can be thought about as having some amplitude and some phase relative to some phase that we call the quadrature. So either I talk about the quadratures, which in this case are the x and p, the initial x and p variables, or I talk about the amplitude and phase. And of course they're interrelated, good point, right? So the amplitude is the, you know, the bagger and theorem length of that vector. And the phase is the argument of this, the imaginary part of the ratio in x. That is to say, any harmonic motion can always be expressed compactly in terms of a complex amplitude. So the complex amplitude encodes the amplitude and phase and the quadratures. Either I talk about it in terms of real and imaginary parts or I talk about it in terms of polar representation of that phaser, right? So if I have a complex number, which is, here's my complex plane, it has a real and imaginary part and those real and imaginary parts are the x and p variables, or equivalently that complex number has an amplitude and a phase. I want you to keep those things in mind because that aspect of the simple harmonic motion, that classical aspect has quantum analogies and quantum features and they're often forgotten. We learn about raising or lowering operators but we have no idea what that means relative to classical oscillators. They mean something, okay? So what this says is that written in terms of the complex amplitude, simple harmonic motion is just the rotation of this phaser on a circle. The amplitude is constant given some initial energy that energy is concerned and that energy is just given by whatever the characteristic energy of the system is times the square of the amplitude. And the trajectory is thus a trajectory on a circle in these dimensionless units, in these scale units that rotates at an angular velocity and will make that. That's what that means is that the position of the particle as I project on this is oscillating back and forth and the momentum of the particle is oscillating back and forth and they're oscillating back and forth 90 degrees at a phase with one another. So when the position is at its maximum value the kinetic energy is zero. When the position is at its minimum value the kinetic energy is its backbone value. You know that from basic simple harmonic motion. So that's the classical problem and I want you to think about it. I want you to think about the complex amplitudes. I want you to think about what the real and imaginary parts mean what the amplitude and phases mean. All right. So then what we did is we said okay now we're going to quantize this and the way we just quantize it is to just say now my position and momentum, canonical coordinates become the position and momentum operators which no longer commute. They have the canonical commutator and now we have one more constant than the problem, HR. Before we just had two, mass and frequency. Now we have the third one, the characteristic unit to action. So it's natural to define the characteristic position momentum variables to be related to one another such that they are equal to the characteristic unit of action and quantum mechanics, H1. And now we've got three constants and three characteristic units and so we can define that. We get the natural characteristic energy scale of the harmonic oscillator HR omega and these are the characteristic scales of position and momentum. Okay. And so express in terms of those characteristic units we now have a dimensionless position and momentum operator. And moreover we have a quantum analog of the complex amplitude. So what was the complex amplitude, the complex number in the classical mechanics now is a non-hermitian operator in the quantum world whose permission part is the position and whose anti-hermitian part is the momentum. And you won't keep that in mind. What is different of course in quantum mechanics is that where it's alpha in alpha star where it's numbers now A and a dagger are operators and they don't commute. Okay. And their commutator is the canonical commutator. It's another way of writing this commutator. So express in terms of those dimensionless variables are Hamiltonian. Here's our characteristic energy scale X and P or in terms of the complex amplitudes looks like this. The point is that because A and a dagger don't commute we have a symmetrized form of what was here. Okay. So there's a new operator that appears to character the amplitude squared the square of the complex amplitude classically is the thing we call the number operator quantumly. I think quantumly should be an adder. And that thing, the number operator for reasons we know that its eigenvalues are the numbers the natural numbers has these commutator relations with A and a dagger. And we use them to solve the time independent Schrodinger equation that is to say to solve for the energy eigenvalues of the Hamiltonian. Okay. Because the energy eigenvalues are the eigenvalues of the number operator multiplied by A for omega that's a half, right? And what we showed in lightning speed at the end of last lecture is that those, that number operator its eigenvalues are the natural numbers the non-negative integer 0, 1, 2, 3 all the way up to infinity. Okay. And so the energy eigenvalues of the simple harmonic oscillator are A for omega times n plus a half. So the energy eigenvalues are, yes? Were there any other potentials that have the same space in the same way? No. Absolutely. That's a good question in the answers. So this, as it was noting, of course what is unique about or what you see about the harmonic oscillator as in fact is unique to it is that the energy eigen, the energy levels are equally spaced. They're all spaced from one another A for omega and that is unique to the simple harmonic oscillator that is a feature of the simple harmonic oscillator. If you have that, you have a harmonic potential. Of course, the lowest energy state is the ground state and the ground state is the state with 10 to the power of 0 and it has an energy that's a half A for omega above the volume potential that's called the 0 point. Okay. And moreover we showed the algebraic properties of the A and A dagger which we call the raising and lowering operators or lowering and raising operators. That's to say those operators take one of the number eigenstates and either lowers it by one or raises it by one. Okay. And of course there is a ground state that's how we derive this fact and that ground state has the property that it is annihilated by this. This is why sometimes this is also called another name and it becomes more important in the context of field theory when these ends are quanta of excitation of the field of our particles then this is known as the annihilation operator A dagger is the creation operator and with this, these two properties what it says is that I can obtain any of the energy eigenstates the number states by applying the creation operator or the raising operator to the same thing end times to lowest energy level the ground state and then we have to re-normalize it because this is not a unitary it doesn't preserve the norm of this and we re-normalize it and that norm and factorial it's easy to check So just come back to the front board here for a moment what it's saying is that quantically whereas classically sort of any, remember we said the radius of this circle represented the energy of the system and the system starts there and just rotates that the quantum state says in some sense there's quantized possible trajectories in phase space all separated by the department now of course it's not exactly true because I don't know it's supposedly a circle but you get the picture because of course I can't be at a point in phase space I mean there's a kind of uncertainty above over here and there's some kind of we're going to talk about this in much more detail think about this uncertainty here X and P in these guys but loosely that's a good picture of what's going on and the reason you can think about the existence of the zero point energy is as we discussed when we thought about the particle in the box it's from the uncertainty principle it's impossible to vocalize at position animal matrix if the ground state were just that would have that position and no kinetic energy that's impossible but the ground state is the minimum energy state that consistent with the uncertainty principle so far so good very good now one thing we can see from here firstly is that what we call the number states which are the eigenstates of the number operator which are also the energy eigenstates of course here n equals 0 1, 2 a form of basis we know that the eigenvectors of any permission operator form an orthonormal basis and so and of course in the context of the electromagnetic oscillator unlike say a finite square wheel all the states are bound there are no unbound states so this is the complete basis so a resolution of the identity can be written in terms of the number states and that is to say a basis for Hilbert space and what is Hilbert space in this case is the space of square normalizable functions that is the Hilbert space we have been talking about one dimensional mechanics of a single particle so this forms a basis for Hilbert space which means that any observable or any operator I should say can be expressed in this basis so for example we can write the position operator in this basis we've written position and momentum in terms of continuous variables the x eigenstates and p eigenstates but we can and we often do write them in terms of discrete variables the number states so even if I'm not talking about the simple harmonic oscillator this is a basis right it doesn't matter whether they happen to be the eigenstates of the Hamiltonian it's always a basis yes Steve, do you have a question? yeah I know physically the annihilation of any of the operators cannot hit any people at equal zero or yes but my question is it does seem like any people change if you make a negative apart from the fact that you get imaginary terms the reason that those states don't exist is the following n itself is a positive operator meaning that its eigenvalues have to be positive and we saw that last time as because if I look at the expectation value of n with respect to any state that is equal to and that is equal to the norm squared of this vector which is always greater than or equal to zero yes but if you make n like negative 2 but then n would have a negative eigenvalue and it can't so that's how we got to that very good so because of the basis let's write the matrix representation of x and p we can do that so what about x and p how do you do that well whenever you're dealing with the number of basis the thing to do is express things in terms of a a a dagger because we know how a a dagger act on this is x in terms of a a dagger thank you very much so it's the real part with the factor of 2 in there I don't know if this is correct okay and p is what the imaginary part so that's a minus a dagger over 2i so if we know that then we can express x and p in terms of this basis because we can always write a a dagger in that basis, let's do that first okay so let's look at for example the annihilation operator in the number of basis so I'm just going to insert a resolution of the identity on both sides so I'm going to have the sum over n and n prime so this is equal to the square root of n n minus 1 delta n prime n minus 1 so this then is equal to the square root of n but because I can't have n less than 0 n equals 1 to infinity n minus 1 in the case where n equals 0 doesn't exist because in fact it's 0 so that's important sorry and a dagger is the adjoint that's just taking the adjoint or if I want to just relabel things and start at 0 I can do that too let's just relabel the sum so one of these this is just expressed as a set of our products and you see what this thing does it takes n to n minus 1 with that coefficient or I take n to n plus 1 with that coefficient let's write them as matrices of course these are all matrices so we can't write down a whole matrix but we'll write down a few of the matrix elements of it so our case is elements 0, 1, 2 dot, dot, dot of course it has nothing on the diagonals column 1 column 0, column 1, column 2 and then it has something on the off diagonals and you tell me is it on the upper diagonal or the lower diagonal lower if we see here this is row column right so it's root 2, root 3, dot, dot, dot 0 is everywhere else exactly so a dagger looks like and so x is this plus that over 2, root 2 and p is this minus so we'll have things on the upper diagonal and the lower diagonal so we can write x and p as matrices these unlike the position in momentum eigenstates the number states are valid states of Hilbert space that's why we get a representation of x and p as matrices they should be because this Hilbert space it has a countably infinite basis here's an example of such a basis right good um please so you're saying that in this basis the x is just better to hate I'm just trying to you know all I'm saying is that it has the behavior that we don't expect from any operator on a Hilbert space it's a matrix the fact that we expressed it I mean let's talk about the position of momentum basis okay so let's talk about so now I'm going to these are the eigenstates of the number operator now we can look for the position in momentum representation so the way we said that we looked for states that are eigenstates of the x operator and the p operator now these are continuous variables but that's okay they allow us to write a resolution of the identity so that's okay and let's see now so whereas these operators expressed in this basis have matrix elements that are just numbers in this case the matrix elements of x and p have singularity in them right this x is up so it's in some sense not very well behaved right and p in that in the representation p eigenstates the momentum operator in position representation was the derivative from operator I'm sorry the position operator in momentum representation was the hr went away because this is dimensionless units this looks a lot like what we did before but in the character scale that's correct that's exactly what it is indeed let's just just emphasize that let me say one quick point recall that with the units of the problem the kets and p at units so recall with units we had these are my little variables having units which meant that this thing as units of one over the square root of length and p kets has units of one over the square root of momentum which is the square root of momentum operator so I can define the dimension full ket in terms of the dimension less ket as one over the square root of the character is the unit where x is equal to xc now this thing has units or said another way the dimensionless ket is related to the dimension full ket so by getting rid of the units then when you do the change of variables this so if I look at for example x prime in the dimension full variables they said that was h bar over i d by d x delta x minus x but if I wanted to do all that re-expressing over here this is going to be you know there's going to be a one over root x that gives me xc put it over here and then I get p, one over pc moreover of course what we have is that I can talk about position and momentum representations I mean let me just quickly go back over here before I say of course in the number of basis that I can write any the state as an expansion over the number I'm in states and the c sub n's are just the probability amplitudes in the end basis with respect to the continuous variables we have a similar thing but I start to write every side as a superposition of position I do vectors that way or momentum those are the position and momentum wave functions so psi of x is that which if I wanted to write it in dimension full form is that times that full variables gets rid of that and the momentum space in dimensionless variables is finally what about a and a dagger well what I can see is let me first say the following thing if I look at the momentum operator acting on a state and look at the wave functions we get the derivative respect to x so the momentum operator is the derivative of acting on the wave function or in momentum space the x operator acting on the state looks like a derivative with respect to p so what about the creation violation operators or the grazing and lowering operators what do they look like in position momentum space they are combinations of x and p so let's just do it so if I look at I can take the annihilation operator and I act it or lower an operator and I act it on the side what is the wave function well to do that I look at the most position representation so that's equal to the position represent a is x plus i p so this is equal to x let's write it all out 1 over 2 x on side taking the position representation of course so good what is this it's x times the wave function and what is this it's the derivative the momentum operator in position space is the derivative all these x's are the the new dimensionless everything to dimensionless sorry yes probably be quite much more careful about my notation here plus i times the derivative perspective so in the position representation the annihilation operator acting on this is x plus the derivative respect of x what about and of course a dagger is just the adjoint of that and the adjoint of the derivative is minus what about in momentum space what is the position the creation of the annihilation operator x plus i p in the momentum representation and what do we get this guy he's got some minds in there you gotta think about it 1 over minus i d by dp and then what is this guy i times p thank you very much times the momentum space so in the momentum representation this is i over root 2 p plus d by dp up to this overall phase of i the annihilation operator and the position of momentum representation look the same which you kind of expect because they're kind of symmetric in x and p except an overall fact some i's floating around there and of course a dagger if you put the minus sign there very very good alright so given how do we find the position or momentum representation of the energy eigenvectors that is to say the wave functions that are the energy levels associated with the energy levels of the ionic oscillator we could so one way we could do it is that we could express so we see the position or momentum representation of the energy eigenvectors now one way we could get at them is to solve the differential equation i over root p the wave and so you know sorry i mean what that would you know one way is to say there's a differential equation in the position representation we know that uh the wave function so this is the time this is h side equals e side and we could just try to solve that differential equation which is the way it's always done or used to be always done in introductory quantum mechanics you plug in a power series and it seems the power series eventually has to truncate because you can't satisfy the boundary conditions unless that and that's one way to get at the eigenvalue equation that we got algebraically just based on the theory of operators and positive operators and so forth but another way is to use the one thing we know which is that there is for the ground state we have a very simple equation it says for the ground state we're calculated by the lower component we can express this equation as a differential equation and just solve that and once we have the ground state we have all other states because all other states are obtained by just raising that n times so what we're going to do is do that much easier and let's just do that but I agree this is perfectly correct alright so how are we going to solve this equation from the wave function what we think is the wave function u0 ground state wave function n would be 0 so we don't want to solve this equation we want to solve that equation so how are we going to use this equation to find u0 if I did that I'm going to get 0 equals 0 say again yeah I want to express this in the position representation that's what I want to do I want to link that this equation because that's going to be a differential equation and we have that over there somewhere the annihilation operator in the position representation is equal to 1 over root 2 x plus the derivative with respect to x on the wave function which is what we're calling u0 alright, good enough ground state satisfies the following differential equation x d by dx ground state wave function is 0 so that's a simple differential equation we can solve but we can solve it of course this is really in 1d without time dependence it's a simple PDE not a PDE so how do you solve that differential equation separate variables thank you very much this says that the derivative with respect to x is equal to minus x which says that the integral x squared and this is the natural log of u0 divided by some constant a so we have a solution the ground state wave function we just call it some constant what is that function? it's like a homework it's a Gaussian how do we find this constant c? normalize it very much excellent alright, so the norm of vector squared we can do as an integral in position representation so that's minus square equal to of pi I know if it was over 2 it would be yeah I think it's this do you do like square root of pi over whatever in front of you? yeah, that's right that's right I only know when it's normal I just move c and you move c okay, it's good alright, and we want this to be equal to 1 normalize it alright, so where would you c be? now of course there's an overall phase that we can always put in front here but by convention we choose this to be we do that okay, so that says in dimensionless units u0 is 1 over the fourth root of pi e to the minus a half x squared in dimensionful units I have to put in a 1 over the square root of that putting in what xc was the characteristic remember xc was the square root of hr over m omega this is equal to hr over m omega and pi to the 1 over the power e to the minus a half and x squared yeah, so I mean I guess to classically think about a harmonic oscillator I would expect it to be most likely to be found where its speed was approaching zero at the ends and not in the middle where its speed is the highest indeed, that is an excellent piece of optimization and that is something which is saying that this kind of motion is extremely non-physical now, I was going to say this first next section but let's talk about this now so let me hint at something so azic was let's think about a pendulum a pendulum that's a sublimonic oscillator spends a lot of time at the turning point and then is speeding through the center so you kind of expect the highest probability for it to be is at its turning points and the smallest chance of finding the particle to be in the center this is the opposite if I look at the wave function is it because here when it has a tip of the swing it's just very narrow but so nothing must go from very large no, you cannot talk about the problem is you can't talk about the position and momentum simultaneously classically so this is this wave function supposed to be a bell shape this is the square of the wave function so classically we can talk about the position at a particular I mean the momentum at a particular position we can do that classically because we can talk about position and momentum simultaneously and what is that given a certain amount of energy well it's whatever the kinetic energy is at that point of the momentum so that's the square root of 2 and v-8 right so where the energy at the turning point the momentum is 0 right and you expect it to stay there all the time now what we talked about very briefly but we did talk about this is the WKB approximation is a way of writing down the wave function when the momentum is large compared to the characteristic scale of change of the potential so when the the wave plane was tiny compared to something having to do with the rate of change of the momentum in this case this is the spring constant so for very very short wave lengths which in this case means high energy we expect the following to be true that this is equal to 1 over some constant normalization constant divided by the square root of the classical momentum either the I or the classical momentum remember this so this is a semi classical approximation so we expect this to be true which is to say that for large energies where the the wave length is very small so here's my harmonic we have the ground state the ground state wave function looks like that we'll talk about the intermediate cases in a moment but if I'm at large n well then this should be an approximate wave function which means the wave function should have a lot of its probability amplitude where the classical momentum goes to zero and very very little a little bit so up here I mean classically the probability goes to infinity small number here very high this is the classical probability based on this amplitude and what we get is something that looks like this supposed to look symmetric I'm sorry so there's a limit of large quantum numbers that's to say a high energy we have a limitation that you intuited and that you expected the probability amplitude should be very high at the classical turning point and very small at the place where it's speeding by the fastest the classical dynamics is informing in some way what the wave function is okay and we saw that when we looked at how the amplitude I mean at phase of the wave function obeyed equations that were the classical Hamilton Jacobi equation okay so this is sometimes known as the correspondence principle now I wonder we're going to talk about this a little bit more and try to understand that somehow at the limit as n gets large I should just say whatever the potential is n is large to get to the classical limit now that's what we mean by classical is a very slippery term in the sense in which this state is supposed to be symmetric is a classical state well that can you think about the semantics of the word classical but what is certainly true is that this is true as to say the wave function is well approximated such that its magnitude is guided by the classical trajectory but for short I mean for long wavelengths for low quantum numbers the wave nature of the motion dominates not the ray trajectory in which case it has nothing to do with the classical trajectory nothing excellent, excellent optimization so we have the ground state what about the higher excited states well firstly what can you tell me just from what we know about the nature of the potential and the solutions to wave mechanics at 1D about what you kind of expect the ray function to look like yet it's got another node so you kind of expect it to look something like that right and then what about the next excited state mean it's supposed to be there kind of like something like this and you know that this is symmetric and isometric symmetric and isometric okay it could be one two why am I saying that the eigenfunctions of the Hamiltonian are necessarily symmetric and isometric functions of X potential is symmetric potential is symmetric potential is reflection symmetric and thus we know that the eigenfunctions are eigenfunctions of parity alright very good okay so algebraically we have this which means that the eigenfunction is given by and so this is the nth power of a dagger which is over there a dagger in the X representation so this is 1 over the square root of n factorial 1 over the square root of 2 to the power of n X minus d by dX n times acting on so we just have to do that but the answer is that this every time I take this do this derivative well I'm going to get the Gaussian back because you take the derivative you get the Gaussian and then you're going to get some derivatives of the things in the exponents which are going to be polynomial in X and so this thing is equal to some polynomial the nth polynomial X times the Gaussian and these polynomials have a name they're called the Hermite the Hermite polynomials I have to double check the fact because the Hermite polynomials have a certain factor yeah I forgot that stuff okay so this is equal to this I'm just going to write my name so those are called the Hermite polynomials and the Hermite polynomial so by definition I could write a Hermite polynomial as what I did when I take this derivative and times on the Gaussian and then get rid of the Gaussian part so here are some of the Hermite polynomials H0 is 1 H1 is linear H2 is quadratic notice they alternate from even to odd functions so H and use the reflection symmetry I either get plus or minus and this is what they look like you take those polynomials you multiply them by Gaussians and you get these are the odd functions now I'll leave it as a simple exercise for you to show the following that in the momentum space representation so and then before I do that let me just quickly say in the position representation is equal to some normalization constant a sub n times the Hermite polynomial either the minus x squared over 2 and if I write out all the factors here that in the dimension full version if I had to talk whatsoever just in a drawer putting back all the units here to 1 over xc xc either the minus x or 2 what about in the momentum space well firstly we can see right away what is this well again we start with the equation that we annihilate the ground state and in momentum space this is an annihilation operator times i over root 2 and this I can cancel so what can you tell me about the momentum space wave function of the ground state look at that equation for position space same it's exactly the same in these characteristic units so in the characteristic units this guy is exactly the same it's exactly the same Gaussian it's also Gaussian in dimensions units with exactly the same width therefore what are the excited states they're exactly the same except there's some factor of i by convention so this thing is again whatever normalization constant I have her mean polynomial up to that phase convention they're exactly the same and this again is unique to the simple harmonic oscillator and the reason is that in the simple harmonic oscillator x and t are the same the simple harmonic oscillator in the Hamiltonian was x squared plus e squared in some units this is also true for p so the position wave functions look just like the momentum wave functions they're the same it's the symmetry in x and p that makes the simple harmonic oscillator special alright we shall continue this discussion next time


The study found that children who ate school lunches based on the new Nordic diet had higher average food intake than those who brought packed lunches from home. However, the amount of food left uneaten was similar between the two groups. Additionally, the study showed that children's reported likings of the meals were positively correlated with the amount of food they consumed. Furthermore, the study revealed that certain types of meals resulted in greater amounts of uneaten food, such as soups and vegetarian meals. Finally, the study concluded that portion size should be taken into consideration when designing new school meal programs. This article was authored by N. V. Forsen and D. Lassen, Elizabeth W. Anderson, and others.


Many educational shows around the world are usually made to promote positive messages, like having a good education, good manners, and being nice to people, even if they are of different races and religion. The show I'm talking about does not teach these good values to children. Rather than promoting diversity and tolerance towards any person, it instead shows anti-Semitic and anti-Islamic propaganda. The show, in question, is called Tomorrow's Pioneers. The show was first aired on April 13, 2007, and it continued to produce more episodes until October 16, 2009. It was created in the state of Palestine, by Hazi Malshari. The show is aired on Al-Aqsatidi, a Palestinian Hamas-affiliated television station. What many people remember about this show is the bootlegged Mickey Mouse character, named Far Four. The character promoted anti-Islamic and anti-American beliefs, and was shown imitating the use of AK-47s and grenades. One of the episodes showed Far Four copying a test and getting scolded by his teacher. The reason why Far Four cheated was because the Jewish people destroyed his home. When the house got destroyed, Far Four couldn't find his notebooks. Unlike many of the scary stories on the internet, this one is real, and unlike many of the stories that falsely claim that they're real, I will show proof. You see, the show is first widely shown to American audiences on news channels like Fox News. These news stations reported the anti-Semitic and anti-American beliefs, shown in his television program. Far Four is the main point in the news station's reasoning on why Tomorrow's Pioneers is seen negatively, because like I said, cheaply imitates an American icon known as Mickey Mouse, and using him to spew hate messages. That is not all the show has to offer though. Looking it up shows you more things about the show, and other plots in it.  It sickenes me that people had made this filth, all because of racist beliefs made by Hamas. It's the reason why Disney is so up in arms about protecting their icon. It's not because they are greedy, it's because they are afraid of this happening to their poor Mickey Mouse.