Welcome, everyone. Thank you for joining us today for this panel, The Asian Art World and COVID-19. We're so grateful that so many of you could join us from so many places across the world today for this very topical and very important subject for today's art world. My name is Malcolm McNeill and I'm the incoming director of the SOAS Postgraduate Diploma in Asian Art, taking over this summer from Dr Heather Elgood. And I'm also a senior lecturer in arts education at the School of Arts in SOAS here in London. The SOAS Postgraduate Diploma is a unique programme, centred on object-based study and underpinned by rigorous scholarship. The programme sits at a nodal point in the overlapping fields of academia, the museum world and the art market. And it's in that spirit of connectivity that I take great pleasure in welcoming our expert panel today to join me in discussing the Asian Art World and COVID-19. Our first speaker is Mr Calvin Huey. Calvin is a cultural entrepreneur. He is a gallerist, a curator, a collector and among many other things a connector of both people and of ideas. He is based in Hong Kong but active across East Asia and here in the UK. Calvin has numerous strings to his bow, including but not limited to his role as co-owner of 3812 Gallery and as founder and director of Ink Now, a cultural brand dedicated to contemporary ink art through a raft of publications, exhibitions, events and award-winning expos. Thank you very much for joining us today Calvin. Our second speaker is Anna Jackson. Hi. Keeper of the Asia Department at the Victoria and Albert Museum, the world's leading museum of art, design and performance. In addition to her long-standing leadership of the V&A's Asia Department, Anna has curated several groundbreaking exhibitions addressing subjects and material from across Asia. Her most recent project is the critically acclaimed exhibition Kimono from Kyoto to Katwok, sadly currently shuttered as part of the UK lockdown in response to the current pandemic. Our third speaker is Jonathan Stone, Christie's co-chairman of Asian Art and deputy chairman for the Asia Pacific Region. Jonathan leads Christie's global specialist teams in Asian Art, covering auctions, private sales and particularly topical in our current climate e-commerce, while he also supports the auction house's broader activities and initiatives across the Asia Pacific Region. Our final speaker is Victor Wong. Victor is a pioneer in the truest sense of the word, with a long and illustrious career in computer-generated imagery, not only exploring but creating new spaces through digital design. Victor more recently turned his hand to ink painting around five years ago and has since developed the world's first artificial intelligence capable of producing Chinese traditional ink painting materials, which Victor has christened Ai Gemini. Victor has told me he views his process as collaborative, blending man and machine, combining the agency of both human and artificial intelligence to produce starkly original objects and arresting images in brush and ink on paper. As a true digital native, I look forward to hearing Victor's views on the implications of COVID-19 for the Asian Art world. And now my opening question addressed to the whole panel, how is COVID-19 impacting you or your organization and how are you adapting? Calvin. Hi, good evening, everyone. Thank you, Soa. Thank you, Malcolm. It's my pleasure to speak in this panel today. Well, I believe the COVID-19 pandemic causes a lot of changes to everyone. I think we're all now facing it. I'm now in Hong Kong. I have a gallery in London and Hong Kong, and also I run Art Fair and also our platform called Ink Now, which started in 2019 in Taipei and Shanghai and Hong Kong. Originally, we planned to bring Ink Now to London this year. And also we have a full program of exhibitions and also other activities throughout this year. However, I think like other institutions like museums or auction house, we do need to respond to this situation and then to adapt and then change our plan. Well, during the last few months, I think from different aspects, I do adjust and also work with my team very closely. I think on one point is about emotional management because in the UK, I know it's locked down and in China, in Hong Kong, in Taiwan, we cannot travel and I have staff in China and Hong Kong and also colleagues in Taiwan and London as well. This time, I think very importantly, we work very hard together. We reconnect with values of faith, hope, love and nature. This is also something that we already always remind ourselves. This is a very difficult time, but then we gather the positive energy and then we work together. We keep ourselves busy and very high morale. So in the last two, three months, actually, our gallery has launched various new initiatives. For example, online viewing rooms, online kind of discussions. We care about the relationship with artists, particularly during the difficult times. So we communicate with our artists very regularly and we launched Artist Diary to give them a platform to share their views and experience and also to share with our collectors and audience how artists work or live during this time. And we got a very positive feedback from our collectors and audience. We also have launched various new columns in our website and social media like art piece, ART article, and also we have a constant newsletter to engage with our collectors. We also published a lot of articles and news in WeChat and also our social media platform. So we hope very soon, like in China, they already began to resume back to normal in Hong Kong. We also bit by bit, our situation became improved and then we are now planning to reopen the gallery in Hong Kong and London on the 15th of June. So on the slide, you can also see how we like to engage our staff, colleagues, coworkers, and also our partners and collectors. From in this triangle, I try to also consider or to develop something more meaningful based on the artistic production and then we have to also reconsider the curatorial adaptation and how we engage the collectors in this pandemic moment because we lost the connection of the face-to-face physical connection and face-to-face interactions, but then we also still need to run our operations. We still need to launch our projects. We also try to tell the market and tell the collectors and tell the artists that we positively face this challenge and then we find different ways to tackle and also to overcome this. That's why we are now launching this new theme call, Reconnect, because we believe that during this time it is so important that we have to rebuild the connection between people and countries and also between human and nature. So the other thing is talk about curatorial adaptation. So we are specializing in Asian contemporary arts with a focus on ink and we also initiated the notion of Eastern origin in contemporary expression. During this pandemic time, especially the period of uncertainty, I believe people tend to look for spiritual inspiration or spiritual enlightenment. For example, when we look back on the 1950s and 1960s after World War II, many people, especially in Europe, they became very interested in Eastern thoughts such as Zen Buddhism because I believe they like to also get some kind of comfort or mindfulness or contemplation through art and then to get inspired to review what's going on in the current situation and also to move on to a new page of life. So when I mentioned this spiritual abstraction, I also quite strongly believe that after this pandemic, the culture of Asian culture or the components in the Asian arts, we talk about the spirituality will become more and more, I don't want to say popular, but maybe more and more people will be reminded. This is also another shifting trend that we may also foresee. So in next month, I'm very happy to announce our artist Xiao Qin will be having his major solo exhibition in Madrosko Arts Center as the celebration of his 85th anniversary. So two spiritual abstraction masters from East and West meet. I think this is also quite a perfect timing that we can also study this artist's work to review the spirituality from this artist's work and to reflect and to see what happens now in the world. And then this is also the time for us to rethink many different aspects of our life. So I would say maybe the pandemic will also accelerate this shifting trend to call for the understanding of the cultural identity, to call for the understanding of our history and also our cultural origin and also to address the need for balance and harmony in life. I think this is also the moment for more and more Chinese or Asian artists to introduce or to give more exposures of their spiritual pursuit through arts and also to rethink the relationship between human and nation through arts. So as a founder of the art fair and the platform, Slide 3 went to Gallery, Inc. now and previously, Inc. Asia, I believe the Eastern origin has also helped us to reflect the history and tradition to question the reality. So perhaps the globalization of art in the next stage will also bring cultural diversity, especially from the Asian side. And another topic that maybe we will not avoid is about the virtual economy or the online engagement. As a gallery or the art fair platform, I believe this time the technology is so vital, so important. I should see the importance of the integration of art and technology, which is not just from the technical or business side, but also how technology reshapes the art world in, for example, artistic production to collectors engagement. In this slide, you can see, like the right hand side, in the last two months in China, during this COVID-19 pandemic, there are over 300 museums in mainland China launched over 370 online exhibitions, and 12 museums organized almost 100 live streams, achieving over millions of audience. So to us, online engagement is a trend, and we also need to try and try out and develop more unique contents to engage the new collectors, particularly the millennial generations. But at the same time, I also see it is also important to engage the general public. The integration of technology will also enhance the art education, and also the appreciation of arts, and also the community engagement. So I found this is a very difficult, but also interesting time, and as art market professionals, I will definitely continue to work with our colleagues in this panel to explore and discuss further how the Asian arts market will rise in a global platform. Thank you. Calvin, thank you so much for such an in-depth and rich response to that opening question. I'd like to move on now to pose this question to Anna. How have you at the V&A been impacted by, and how are you adapting to the current climate of COVID-19? Okay, well, thank you, Malcolm, and thank you very much for asking me to participate in this wonderful panel. Well, the Victorian Avenue Museum is a vibrant, dynamic institution. We welcome something like 10,000 visitors a day from the UK and around the world to the Museum of South Kensington, and of course, more to the Museum of Childhood and V&A Dundee. And these people engage with our objects in our permanent galleries. They see special exhibitions we put on. They participate in events, and they just enjoy the cafe or the shop, or particularly at this time of year, the garden. So of course, now we've just, we had to close our doors. I think our last day was the 18th of March, just before lockdown. So now the Museum is quiet and dark, and only our security staff and the state staff are monitoring the galleries for us. And this is really very painful for all of us. I mean, our resin debtors, every instant we have as a public museum is to have our doors open, because we're there to share our collections and our spaces with as many people as possible. And for me personally, it's been very painful because, as you mentioned, we've just launched our exhibition, Kimono Kiyota to Catwalk. This is four years of my hard work, and to see it close after 19 days was very, very sad. And this is one of the saddest pictures I have of my colleagues in the textile conservation section covering up the objects to protect them from dust while we had our closure. And also, we shouldn't really think, we have to think, there are mammoth financial implications for the V&A for every museum in the world because of closure. And that's a big challenge we'll have going forward. But for now, although our doors might be shut, we remain open. Next slide, please. At like many museums, we've reached out through digital means to our existing audiences and hopefully to new audiences. We're lucky in the V&A that we have a very well-established website and social media channels. And really, we've just sort of thought of new ways of engaging with audiences. I think, obviously, the number of people who are sort of accessing material from the V&A online has risen dramatically. We now have 3.5 million social media followers. And with our social media posts, one of these you can see on the left, we tend to do quite quick and quirky kind of content, which is really inviting audience participation, inspiring sort of creativity out there. We also have sort of more focused look at aspects of the collection. We send out e-letters to those who've subscribed. We have a dedicated YouTube channel. So what we did for the exhibition, just before the tissue went around those objects you saw in the previous slide, we quickly made a film. I think we filmed for about three hours in the exhibition, just me and two photographers doing a tour of the exhibition, which we now edited into five short films. And they went live a couple of weeks ago. And we've had 215,000 views, I think, by now. And again, very, very positive response to that has been great. And I thought I also should mention that we have our own dedicated Chinese social media channels on WeChat and Weibo. And in the middle here, you see just one of the initiatives we've done that we do very dedicated kind of material for our Chinese social media. And in fact, we're the only Western museum to be ranked as one of the top 10 museum profiles on these channels. And this was a particular sort of competition we ran in April and May, which was to people to style themselves up as a V&A poster. So these are famous posters from exhibitions, including Chinese paintings there, David Bowie, Hollywood Costume, Horst, and Frida Kahlo exhibition, Making Yourself Up, where people sort of reinvented them rather cleverly. So that's very first sort of, again, inspiring sort of creativity in our audiences. And I think it will be very interesting to see what happens in the future about how whether all this use of digital media is really will really change the way we engage with our audiences going forward. But of course, for now, we are hopefully planning for the reopening of the museum, which we're again, not sure of dates exactly, but hopefully in the next couple of months, we will be welcoming physically people back through our doors. Thank you. Thank you very much, Anna. Now, Jonathan, to turn to you. How is COVID impacting Asian art at Christie's? And how are you adapting to the current situation? Great. Well, thanks, Malcolm. And thanks to Sir, as a privilege to be on this panel. I think that the first thing that I was thinking about is it's a very practical things. When the big issues we've had is not being able to travel. Nobody's been able to travel for what is almost six months now. I think this has been a big issue for us because it's really impacted our ability to source material for the sales. I'm going to talk a little bit later about how we have improved sort of digital connections and remote connections. But still, when you're dealing with great works of art and you want to convince somebody to consign to the sale or they want to see you, I think as everybody here knows it's really difficult not to actually go and see the physical work of art. And it's incredibly difficult not to be able to talk to the consign or the person, the collector face to face. So I think that's been a real issue. I think the other thing, of course, has been the degree of uncertainty. Because like everybody, we have to make plans. All of us are making plans for whether there is exhibitions or sales or projects that we're all working on. So I think not knowing what is coming down the road. And I remember that in Hong Kong, back in February, we were thinking this is all going to be over by April. But excuse me, here we are in the middle of June and most particularly is not. Hong Kong is much better off than a lot of other places, of course. But it's this uncertainty and the difficulty being able to plan. As we say, you come up with a plan B, but you need to come up with a plan C, D, F, G and H as well. Because you're really, and this is on a very practical level, I think these have been some of the challenges that we've had. The uncertainty, of course, impacts us because people are concerned about the market, then they're concerned about where the market is going. But I think what is significant for us in our business is that, as indeed was true during the financial crisis of 2008-9, there is an appetite to buy. But again, for the reason of not being able to meet people, and also because of uncertainty, it's a greater challenge for consignors than it is for buyers. Because for buyers, whatever the circumstances, if you have a great work of art, it could be a once-in-a-lifetime opportunity. And they will continue to buy. And there are opportunities, though. Having said that, I think there are actually a few silver linings to the cloud, to this COVID cloud that we live under. One is that it's actually made us speed up a lot of developments, which I think were already happening, but it's actually incrementally increased that. Calvin referred, I think, to online sales and so on, where we've really ramped up our online sales. And they were happening anyway. But now this is very much more part of our daily life. And we've increased significantly the number of online sales and also what is being offered in the online sales. And the online sales have been doing extremely well. And that's not just part of political propaganda. I mean, it's absolutely verifiable truth. They have been doing really, really well. I think it's also made us think more about how we engage people remotely. We have sales coming up in Hong Kong at the beginning of July. And these will be live sales. But many people can't travel here. So how do we engage with them? You have traditional tools, but also there are so many more tools that you can use now that didn't exist before. We've developed very quickly a lot of social media ways of interacting with our clients. There's been a lot of activity on WeChat or the other Chinese media. But it's not just restricted to that. There's a whole range of things that we've been doing that enabled us to present ourselves. And also importantly enabled the buyers to participate in the sales, even if they physically can't be in the room. So I think those are some of the things. But I'm quite keen to think that there is this silver lining because it really has made us think about things that we hadn't quite thought about. And it has speeded up a lot of the things that were coming anyway, but it's actually made them happen much, much more quickly. So there's some negative and uncertainty. But I think on the other hand, there is quite a degree of positivity in a way. And that's what we're kind of looking at. Thank you very much, Jonathan. Well, with that sort of digital pivot, that acceleration of existing moves towards the online in mind and that digital environment, I'd like to turn to you, Victor, as someone who is very much at home in these kinds of spaces, to tell us how COVID has impacted your work as an artist and how you have adapted. So I would like to introduce a little bit of my work and then how the COVID-19 affects my work nowadays. So I come from a background. I used a computer as a tool to create visual work way back in 1989 when I do movies and games and all that. But now I used the AI and computer to create the Chinese contemporary in paintings. So like for a few years ago, I was invited to do a work which is converting animations in painting into animations. So after that, I think, well, computer and in painting, Chinese traditional in painting and AI combined together should be very interesting. So I created my own AI which is now my creative partner to create in painting. So he got a body you can see is a robot arm and I set up with a real ink and papers and water to have him to draw in paintings by itself. So how's the process going? Is that I copy the practice of Chinese in painting. So when we do Chinese in painting, a traditional Chinese, we rendering around, we do other works and then come back and then we thought about what we have encountered and then start to do the painting. It's kind of mind-scape. So I asked at German line my creative partners AI to create a landscape which is virtual landscape first based on parameters like gravity, like erosions, like all that. And then after he created the 3D virtual landscape, he will find an angle because I think movies a lot. I teach Germanize to find a good angle to to light draw the landscape. So he started doing light drawing of the virtual landscape using real paper and ink. So it's come up with some details and the interactions of the paper and then water. So that is something that an AI can create mimicking the process of a Chinese art scholar's painter artist to create a painting. But the problem is that it affects, I mean the COVID-19, 19 affect us because there's so many details in the painting because the interaction between the paper and the ink, I have to show to the collector that how that look, how it's under natural light, how do we create a reality through internet and videos and photos. So I created setup that I can picture and then film the very little details of the artwork and show it to the audience, to my collectors that how fine painting it is. So that is something that changed. But there's maybe cons and pros because of the COVID-19 because it forced me to put the setup and then now I can archive my work and like hundreds of pictures using this archive. And also also I thought about like there's no physical galleries opening that and all that. I create my own museum virtual museum to showcase my paintings like this and I put in virtual reality. I even can create like an ancient Greece like environment that put my paintings on and then people can use the VR and then go there. And also I can go further because not necessarily we see the paintings in the gallery. We can go to the moon like my series said fast after the moon. Why not we create exhibitions on the moon so I can create a virtual moon based on the real data and then I create my exhibition on the moon. And how about underwater? Have anyone have an exhibition underwater with like paintings but I can create an underwater environment to put my paintings on and have it. So this is kind of we have some problems and we overcome it and come up with some extra I will say it it inspires us to do more. And then I will it will have a new path to go into future. I think of course yes COVID-19 affect all of us but it also give a chance to create another path to keep us alive. So this is what I think we should think and react to it more positively. So that's my that's my my reaction to that. Victor thank you very much and thank you all for your very in-depth and diverse answers to that opening question. I think it's very interesting that as Jonathan rightly points out we are also constricted in where we can go and yet Victor as a digital artist is taking us to the bottom of the sea and to the surface of the moon. That's very very refreshing and very uplifting. So a quick follow-up question to all of you if you could answer with maybe one example in response to this this follow-up question. It seems that we're all taking a digital pivot in how we engage with our audiences that whether in museums, art fairs, auction houses or as practicing artists but how much of what you are doing in each of your respective roles is an amplification of what you were doing before and can you give us one example of something completely new that has been undertaken in the face of COVID-19 and perhaps we can start with Anna here on this one. I think what I'm doing on a day-to-day basis is an extension of what I do as a curator anyway. It's a bit odd as I sit in my home to think that there is a public and audience out there but I know they're there and everything I'm doing now is either for that audience now or for that audience in the future. I think apart from me grappling with the technology I think for the museum it's been interesting to think about whether we would collect anything that is to do with COVID-19 and my colleague Brendan called me who's not in my department particularly so it's not an Asian initiative exactly but the idea about what people have asked you do you collect something that's to do with the crisis that is so fast moving and then we don't really know what's going to have meaning for the future but we have started to collect handmade signs so the rainbow symbols you've got a rainbow behind you there but the rainbow symbols everyone's put up in their windows the signs that have gone out either just to tell you that the shop has closed or to raise awareness of a good cause or to sort of just show support for something so we've been sort of engaged with sort of collecting those which is we've got an amazing response to that so that's the one thing I think the museum has thought how could we you know do something that we would normally do curatorially but in a slightly different way. So it's something that's been an existing practice that's been adapted and applied to the COVID situation and Jonathan could you give us perhaps an example of something completely new that Christie's has done in response to COVID-19 or is it all as you said the acceleration of existing initiatives that were ongoing anyway. I think it's honestly the acceleration of many initiatives that were ongoing I think the same with everybody else what is the future going to look like I think this you know this is a this is a big question is the future going to be that we will have 50% of ourselves online for example I mean that would be something new but I to be honest with you about my struggle at the moment sort of predict the future like that and I sure don't have a crystal ball but I think I really do think it's very much about the acceleration and I think you know there are there are new initiatives not that they might not have come anyway but I think that because of COVID-19 they're really happy and accelerating and come down the road much quicker and I think as I was saying it's really forced us to take to take new actions to think about how we engage with people in different ways and you know the question again is are you you know are we going to have to be in a world in which a large number of people will convene in one place in the future. Thank you and Calvin perhaps you could respond from the the art fair side of the art market here. So the new thing to me especially the last two years I have been on the road constantly so these two to three months like everyone slow down give a lot of time to think and also to develop some new initiatives that is already in the plan but previously have no time to to to really go down into details no time to really move things forward so I think this is also this is a good thing for me to really to work with my team to prepare for some new initiatives which we hope to launch in 2021 and also we have also launched like online viewing room and and and revamp the website and also push ourselves like Jonathan said to really engage ourselves in the digital side so yeah something to do being crafted being built so maybe you can share with you later. Great more things in the pipeline so Victor you you told us about AI Gemini you told us about your your creation of a robotic arm with an artificial intelligence that can produce original ink paintings has COVID-19 inspired you to to create something equally innovative and new or are you looking again at um at COVID as an agent for accelerating processes you are already taking on? Well I think as a human as a human when we when we have pressure we react to that and through these reactions we'll come up with a new path and to to it's a kind of survival game now say the collectors cannot see the actual work so how I responded it to have like high resolutions representation of my work and then maybe in the future they would like to have like virtual exhibitions how do they entire go into these virtual exhibitions is it the only way through the internet is there any other ways to do it I'm looking forward for this new technologies coming in as I like a computer artist I use computer all the time and it's ready to go online or offline but it is it's turned out that when we when we face the realities how we represent the realities in the virtual world that is the question so I would like to see more technologies come out how to recreate the realities inside the virtual world that we can go into and then without physical interaction of that and I would see one is that coming out and there will be no return world I mean every one say okay I will go that's Dubai and then I go to Paris and I go to Hong Kong just click and this is somehow it's happening it's happening in the future oh no it's happening now and then we go into the future I would see that okay great that's I mean Jonathan has no crystal ball but um it seems like you do and it's it's great to uh to get those insights from you as someone who's so actively involved in engineering those environments that you predict will all be inhabiting in the next few years and it seems like the conversation has gravitated in a number of cases towards collecting towards this um this relationship to objects in the physical world and the need to see them in person and I think that's a nice thing to come back to after Victor's um prompts that we're all going to be inhabiting a VR environment in the next few years so perhaps um I'd like to address this first to to Jonathan and Calvin because your relationship to collectors and collecting is is subtly but importantly different from Anna's and Victor's that your your modus operandi if you will the kind of engagement with art you're trying to engender is at a very basic level of transaction it's an acquisition of something and a collection of something um and in Christie's as well as in Incnow and 3812 that's very much achieved by this um charismatic almost sort of erratic experience of sharing a space with an object and feeling a sense of real intimacy with it so how do you create that intimacy and how do you within the confines of COVID-19 and how do you do it safely with the current health constraints on on risk of infection and infection control I think that clearly there are a number of ways in which you can visualize an object or you can present an object I mean there's a huge amount you can do is sort of very high-tech photography you can take 3d images there's an awful lot you can do to present an object as it is I mean there's a lot you can do for art in terms of you you create a conditional report you can there's a there's a lot you can present and in a way to be frank that buying remotely is nothing totally new because we we know that at auctions and the past people have been buying without seeing the work necessarily at first hand you know they've been bidding on a telephone or they've been bidding online in an auction we've been having agents to bid so in a sense it's nothing new but as I keep seeing to keep saying it is an acceleration of this prep and I think the way you present the objects will be increasingly high-tech in terms of in terms of the sort of health issues clearly there are restrictions I mean when we have our auctions in a month's time I think there will be restrictions about how many people can fit into a room perhaps you know we have very clear guidelines on you know temperature checks we health decorations registration all that kind of thing so I wouldn't say that there's a tool going to be barriers but I mean there's a things that we need to we need to deal with but there still will be an opportunity of people being able to come in and see an object at first hand which to me still remains important it just in a way it's the management of that process and the management of the time and that that's I think where we have to be very smart so people do feel safe and secure walking into a gallery space you can ask people to wear masks and everything you know there is a lot that can actually be done I think to make people feel much more secure so I think that by a combination of technology and also care for hygiene management for possible a better word this is something that I think we can do we can achieve so I again you know I'm confident that people will continue to acquire and collect I don't think this is something that's going to be stopped by COVID-19 for a second thank you Jonathan and Calvin and in your art fairs and our experts in your gallery how are you able to create that that sumptuous environment but at the same time ensure safety and security from infection well this is the time for us to demonstrate how we provide our services professionally how we interact with collectors and audience with a responsible and also honest manner recently actually we have an American collector client definitely we need to work with him because he and his consultants needs to acquire some us from us and then we work with like Victor actually is a tech Inc to have a lot of like video videos and also high resolution photos to share with with the clients and this is also to show how we can be reliable and how we can be also we give confidence to our collectors and another thing is I believe it's not every time it's not just about self-transession sometimes it's about how you maintain the relationship how you communicate with collectors to respect them also to care about I always say now the first priority is personal and public safety and to our staff to our colleagues and our workers and in the gallery we also have like all the measures of like hygiene and safety face masks we prepare all these necessities to have the clients to come over to our private viewings so in the last two months I cannot complain because we still have clients to visit our gallery so we do all these measures we respect them we give them space and we do the transactions as well in our fair side this is also the moment for us to remind ourselves how important to continue to engage the market and the collectors not just about the selling our pieces but it's also about like education sharing of knowledge so this is the time for it is a test for all of us I think we should also be more open-minded to see and how we can also embrace this time to do something differently. Calvin thank you very much Anna can I turn to you now from a collecting point of view but as an institutional collection the V&A as a museum of art and design and performance has a very different remit than and a very different relationship to the world than the collectors who work with with Jonathan and Calvin what in the V&A's collection and in the V&A's Asian collection specifically do you think could provide inspiration to design that responds to COVID-19? Oh sorry I thought you were going to ask me about physicality of objects there which of course is probably the most important thing for a museum curator and for our audience it's a physical engagement with the objects and I think for all this wonderful digital technology which allows us to reach far more people than would actually come to the museum there is still something to be said for the physical engagement with objects and it's whether you can use any of these tools so you were talking about sort of wonderful photography that you can use now you know to sort of really hone in on objects to give you stuff you know for me I'm a textile person so being able to show all the layers of textile the embroidery the different techniques that are used whether you could use any of that to bring objects alive in a different kind of way to inspire a certain creativity I think for us working in the Asian world I mean a lot of it is about the connections that we have with people in Asia as well as you were saying Jonathan say you can't travel anywhere so you've got to sort of maintain those kind of relationships and those kind of joint projects and those joint initiatives that we can still have for the future but I think the remit of the V&A is to inspire creativity and certainly through sharing our Asian collections perhaps with audiences that aren't familiar with Asia you know that's a very important remit and I think what we learn through these periods where we aren't our doors aren't open I think is a way of thinking about how we might engage in the future and as as Jonathan was saying build on the things that we might have been thinking about already to really sort of engage in a slightly different way but I would never want to lose the physicality the physical engagement with the objects that you have from that's why people come to museums and that difference from seeing something online if you buy something from one of Jonathan's sales you still one you still get that lovely object hopefully arriving at your door at some point and I think for us that's important and also the museums themselves are are you know our social spaces I mean it's about sort of you know I'm sure if you know as to begin with I'm sure there'll be far fewer people will be able to come to the museum and they'll be enjoyed for some people to be able to wander around their own their favorite galleries totally on their own I mean that will be a pleasure for lots of people but for others you know museums are a social space they're about the sort of dialogue that happens between people and between objects and we think that museum is being sort of crowded exciting space and it's going to be a very very different space for a long time and we'll have to somehow adapt that. Okay so what measures will you at the B&A be taking to allow these makers and designers to draw in your collections to access them when when the designers hanging on your door expect to be left back in again to access the reserve collection? Well we we're not sure entirely when we're going to be able to reopen the museum you know we're in the sort of last phase of reopening so obviously we'll follow government guidelines as the government museum we hope that we will be able to open the door sometime in in July and August and obviously we are thinking we're modeling a number of scenarios now and it will be about you know how many people will be able we certainly can't welcome back 10,000 people a day through our doors you know how many people will be able to come to the museum at any one time whether we'll have to have particular routes through the galleries you know the hygiene environment we'll have to maintain and so on and certainly we will but we will still allow people back to see our you know make appointments to see objects that perhaps aren't on display like in the print room or the Asian study room it just we might have to limit groups and in terms of the teaching the teaching we do for SOAS I mean one of the great pleasures of of teaching on that course is that the students are able to come to see objects and handle them and you know that that probably won't be happening for a while because we won't be able to have too many people in this place at any one time but I would certainly hope that we can still welcome people back not just to the galleries but to the reserve collections as well. Thank you very much Anna and so then one last question to the whole panel before we take some questions from the audience in one or two sentences where do you see the I mean we've talked about the absence of critical balls but where do you see the the Asian art world being two to five years from now what are the what is the one big impact to expect COVID will have had on how the cultural and art sector across Asia and the Asian art sector across the world and will be impacted by this virus and we can start perhaps with Victor. I will see artwork will become more valuable than before because when we lost something we'll find that lost things is more valuable now we cannot go in to see the objects we cannot touch it once we have a chance to really see you now it is a now it's a bonus now to see the objects in persons then you will find more time to spend on it and you will find the value on it and you more you know appreciate what the original artist put the effort on so it is kind of something that you lost your physical existence or physical contact with something and you find it more valuable than before so an increase in financial and cultural value of that because if everything does click click click and you can get it it is not valuable enough but when you when you when you have a little chance let's have a one just one chance to go to a DNA for your lifetime maybe and then you find it and you will spend the whole time focusing on every second instead you spend on it great okay um one sentence from you Calvin what's the one thing that will change five years from now sorry uh tag and art um will be uh something really worth expecting um how it evolves and second is um the gallery and also art fair industry I believe there would be some significant changes I cannot predict I don't know but I just feel that uh is is happening so transformation is coming and that transformation will be driven by technology yes okay great Jonathan um I have to say I love Victor's idea and I kind of wish I'd said it but um not not because it not because of the monetary value of the works of art but I love this idea that if you can't if you can see the works of art less often in person they actually become more valuable um in in a in a cultural or in a meaningful sense not just in a um not just in a um monetary sense but of course wearing my commercial hat I sincerely hope they do become more valuable than monetary sense as well so maybe get it both ways um I mean the other thing I really think is I mean the technology the technological changes that we're going through is is are going to be transformative whatever shape they take um I think that the transform transformation of our work because of technology um saying this for the third time has really been accelerated and this this will be the uh apart from Victor's beautiful idea I think this will be the thing that we come out of this situation with Anna well yes I probably wouldn't echo both Jonathan and um uh Victor there I mean I think the new technology will change possibly the way that we engage with with our audiences but we're in a world now where UNESCO reckons that at least 13 percent of museums around the world are going to have to close as a consequence of this because they will not be able to sustain themselves financially and so I think that the world will hopefully wake up to understand how important museums are and the we you know the V&A is just custodian of all the wonderful things that we have there and I hope that people will realize what what value those collections have those Asian art collections have but also what value museums have in the world wonderful thank you all very much for for your contributions and now it's with great pleasure that I can offer some some questions from our from our audience um I'll put a few quite specific ones to you first so Anna a question to you from a number of our our audience members is Kimono going to reopen and in what guys okay well yes um as you can imagine I was very depressed well I thought it might not but yes we are hoping to relaunch the exhibition again I can't quite say what dates but I would hope that the exhibition will be running the three through September on October like every museum in the world we are negotiating with our lenders now to make sure they're happy with their objects staying with us for another few months because they should be you know the exhibition should have been closing at the end of this month um but it will open you know it's all sitting there now so we just have to you know take the tissue off and turn the lights back on but obviously I think we will obviously be you know the number of people we can actually allow through the door we'll we'll actually be able to come to be able to travel to the VNA to see it will be reduced but yes it will should should be there in all its glory hopefully by the beginning of September thank you very much another question posed really to the whole panel by a number of people we've talked a lot about digital platforms for the communication of physical art what about art that exists solely in the digital realm digital art is that something that we will see a rise of in the COVID era perhaps um we can have a response from Victor um and then um and then from Jonathan to start this up well I think the artwork exists early in the 80s so uh it doesn't really matters on digital artwork because it's always online and it's created um but um the new technology coming out it more on just on a screen it would more immersive like in the environment or you can wear a VR and then you go into the digital world so that is something that happening now um I think uh it it will it will get we will have technologies and also platform and also audience for more and more digital artwork to be created in in the near future obviously okay and for Jonathan if you can speak briefly to the commercial worlds relationship to digital art and then Anna the institutional world um I think yes I mean I think I think it must be a given that there will be a greater emphasis or a greater uh response to digital art I mean one of the one of the things that we did talk about in Victor and part of this was the whole role of AI in art um and I have to be very honest to say that I don't think the last person was trying to be competent I think to speak about this but I think that this is so I think this is a really interesting topic and where AI and art go together I think is something that might be used for another topic forum. Thank you Anna. Yes um the V&A is very actively engaged now in collecting digital art we have a department where their remit is neglected but if that one of the first big part of the V&A was actually Korean a Yoon Chang who did a piece can sorry Yoon Kang who did a piece called Casting which was actually a projection in our cast courts which was a it was an amazing experience and it was interesting because the cast courts themselves are a form of reproduction in the way that digital is now a form of reproduction um so that was uh and that and we acquired that piece and it's there's certainly quite a lot of work being done about you know what kind of digital art we can acquire how do you how do you store it for the future which is another challenge of course. Thank you um a question from one of our so-asked post-grad diploma alumni and the curator emeritus of the Renaissance art collections at the Philadelphia Museum in North America Carl Straker he asks in the UK and USA COVID-19 has had a greater impact on minority communities will this dynamic perhaps engender a rethink of how museums present works of art and how universities teach them perhaps Anna if you would like to respond to that from the the V&A's perspective and I'll see what I can from so-as. Well certainly I think the diversity of our collections is something that's very important to the V&A and sort of representing diverse cultures and diverse creativity and I think this will it certainly leads us to think about how we can really encourage that both in our in our collecting in our displays in our programs it's something obviously we've been doing up until this point but I think this is heightened awareness of what we're doing and the importance of what we're doing and certainly in terms of trying to sort of diversify our audiences particularly who visits the museum and even who works in the museum so I think it's a very important point. So to speak from uh to respond to Carl's question from the point of view of the so-as post-grad diploma and as well as a position in the history of art and archaeology department at so-as we have an active agenda to decolonize our curriculum where we are looking to change the the Eurocentric narrative that has driven much of our history as a discipline and indeed across the other departments and other academic methodologies that in that we teach at so-as so we are we are actively working on this but as Anna says the the current global experience perhaps foregrounds the immediacy it accelerates the need for this kind of action to take place and to take place effectively so it's something we're working on and we are we are working to develop ever faster as it becomes ever more urgent in our changing global environment. We perhaps have time for one more question as we're about to run over and this has come from a number of people but a general question about the broader political context in which COVID-19 is occurring particularly and its impact on the the Asian art market whether it's the the US trade war with China or the recent change in legislation from Beijing that affects the security situation in Hong Kong. I wonder if Jonathan and Calvin perhaps could speak to that the impact of the broader geopolitical context in which COVID has happened and how these aggregate factors might reshape the the the the art market globally and one questioner asked specifically how it might reshape the position of London within that that global market. So Jonathan perhaps we can hear from you. Gosh wow okay. I've not I don't feel quite competent at the moment to speak about London. I might defer to those of you who are in London or have galleries in London to to answer that one. I think in the general in the general context I think that the trade war the one of the issues that we've been dealing with was the imposition of a tariff on Chinese works of art going in going into the United States and there are this has been somewhat somewhat mitigated in that the tariff has been reduced and there are now mechanisms in place with without getting into the complications of it whereby you can you you have a sort of temporary import scheme I'm sorry this is a bit technical but there is a scheme whereby you you you can temporarily import somebody and then you don't you can get the tariff rebated if you if it's taken out of the country again but nonetheless for you know our colleagues in New York who source property from around the world Chinese property for the sales there this has been this has been an issue because there has been this tariff imposed by the Trump administration on Chinese works of art of any kind including antiques doing into the US and that's been a bit of a made life a little bit more complicated as for Hong Kong I'm not sure that the change in the security legislation is going to have an immediate effect or I don't even will necessarily have an effect on the art market in Hong Kong because I think so long as Hong Kong remains as good a place as it is now to do business then I think I think there is there is a bright future in Hong Kong and I think just the security law by itself is in my own opinion unlikely to have an effect on that but yeah thank you John I'm trying not to say I'm trying not to say crystal balls again but yeah I'm fairly I'm fairly I am optimistic about the resilience of the market in Hong Kong okay and and now one Kelvin do you have anything to add to that from the point of view of the expose you run in Taipei in Shanghai looking outside of the Hong Kong environment I share the view of Jonathan so I'm still very confident of the Hong Kong markets I also see perhaps growing importance of London market as well because of the situation like the US and all this trade war and in Asia we are still growing markets the the Chinese market is actually booming that's why I think the buying power is still in Asia the more dynamic so I still believe that Hong Kong and London are a vibrant market for yeah for for Asian arts okay that's great confidence and resolution and so perhaps I said that was to be our last question but I'd like to give one one more question before we move on before we thank and close the panel and this is one that was pre-submitted to us that I'm only just getting the chance to get to and it comes from Christie's Regional Managing Director for Asian and World Arts and Chairwoman for Asian Art in London Leila Davos she asks looking back a few months ago when Art Basel Hong Kong was cancelled due to the outbreak of the pandemic Hong Kong seemed to have led the online and virtual platforms for exhibitions sales and events very quickly followed what was the general response and level of engagement this initiative which initiatives worked the best and were the most effective so really this is a question about a virtual environment that is that was created for the sale room and perhaps we can close with thinking about these virtual spaces we're moving into maybe Victor if you have some firsthand experience of this I'd like you to respond to this question and tell us what you felt was most effective about the VR environment in Art Basel and maybe more generally what can we do to change and improve our virtual reality environments as we move forward into an era reshaped by COVID-19 well I think is the speed of the internet now we're talking about 5G if 5G really happens and it will change how you experience virtual world and that means that you have a better representation of the real one so that is something that looking forward to as an artist not as a politician so or whatever as an artist I would say if we can represent the real work in a virtual world correctly and professionally because of the speed of the internet that that will help a lot to recreate the reality we're going to the matrix okay so wow so we're we're moving into a new place a new period a new time and a new way of engaging with art I think perhaps we can close on on that note to say that we are moving into a technologically driven world what we need to bear in mind the importance of retaining an object of a relationship to physical objects one of the great observations as we all dwell on here was the hope and the belief that even if we become more distant from one another and from the art objects in public collections and private collections that will hopefully increase the value both cultural and financial that underpins our engagement with art and I would like to to kind of close on that note as well as the optimistic hope that the technology for engaging digitally will improve so it's with that sentiment in mind but I want to thank each of you once again for taking your time to prepare and participate in this panel and I'll now hand over to my colleague Dr Heather Elgut who will give some closing remarks and thanks. Good afternoon everyone I wanted to say that from the very beginning when I started this program that is these service postgraduate diploma in nation art my principle has been to make sure not only the object but the the people who spoke to the students were the leading experts and wherever we could we would invite them from wherever they are and one of the great responses to this COVID-19 from my perspective is that today for the very first time we have such a panel which not only reaches the expertise of all of you but also the numbers out there all in different parts of the world so this is very exciting for me and at such a moment that I hand over to Malcolm which I have to say for me not the greatest technology person I am not but it is a great moment for me to hand over to Malcolm so first of all I want to thank him for this inspired idea I want to thank Victor and Jonathan and Anna and Kelvin for all that they brought to the panel today and for all of the students who are listening I want to say hello to you and thank you for your time and attention and I want to bring to you just to know that next Tuesday same time 16th of June we are running a six program series entitled the reclusion and cultivation in Chinese art and we also want you to know that although we are charging for this and you can see on the screen the fee we do have the possibility of free places for those who are shielding due to a medical condition and if you send Denise an email or you write to asianart at soas.ac.uk you can actually explain your situation medically or that you have an NHS whatever it is that they give you if you have that situation and we are delighted to give you a free place so we hope very much some of you will join us in our continuation of this very relevant issue that again Malcolm has inspired us to do so thank you all again very much and lastly Patrick somewhere you are and Denise and thank you so much for making this viable and doable thank you


So, where we got to yesterday was that we had reduced the horrible partial differential equation in six variables, which is posed by the time-independent Schrodinger equation for a hydrogen-like ion to this equation here. Sorry, not being premature to this. So, the internal motion had been separated from the translational motion of the atom as a whole, and we had exploited it by using a change of variables for central mass coordinates and the separation variable, and we had used the work that we did with the angular momentum operator earlier on to show that we could express the internal Hamiltonian in this format here. So, this was called R, I think, that's right, for the internal motion. Right, and then I pointed out that this Hamiltonian commuted with the total, with the angular momentum operators, because the only mention of the angles, theta and phi, sits inside this total angular momentum operator, and therefore we can seek stationary states. There's going to be a complete set of stationary states, which are simultaneous eigenfunctions of E and L. Right, so we will also have the statement that L squared on E and L is equal to L, L plus 1, E and L, and then when we're using these stationary states, the action of this operating will be replaced by this eigenvalue, and now we do end up with what I wrote originally, which is that we're going to have a Hamiltonian, which has a subscript L, meaning it's the one that's valid for stationary states, which have total angular momentum quantum number L, which is going to be PR squared over 2 mu plus L, L plus 1 h bar squared over 2 mu R squared minus z E squared over 4 pi epsilon naught R. And this is fundamentally a Hamiltonian analogous, this is a Hamiltonian analogous to that for the harmonic oscillator in the sense that we have now only one surviving coordinate, of our six coordinates, we're down to one, that's this here, the modulus of the separation vector, and it's conjugate momentum PR. So we've made an enormous simplification, made tremendous progress, and we're going to knock this into submission using the same approach as we did with the harmonic oscillator, we're going to define what will turn out to be a ladder operator AL, which is going to be defined to be dimensionless, it's going to be A0 over root 2, I better write this down from notes rather than my memory, because these factors do matter, I PR over h bar minus L plus 1 over R plus z over L plus 1, A0, where A0 is the following not very helpful item, 4 pi epsilon naught h bar squared over mu E squared. So this is an object I'll make it convincing, well let's make it convincing now. What is this object? This is the so-called Bohr radius, so it was introduced by Niels Bohr before there was proper quantum mechanics using what turns out to be a fallacious model of hydrogen, the Bohr atom, and the way to see what these dimensions are are actually to to write to bring this up onto this side and say look this is going to be E squared over 4 pi epsilon naught A naught, now on this side A naught is on the top, not the bottom, so therefore I have to say this is equal to h bar over A naught squared over mu, so out of this equation by putting that E on the top and this 4 pi epsilon naught on the bottom, dividing through by A naught squared to get this on the bottom, so this is something we understand to be, this is obviously electrostatic energy, and what's this that we see on the right side? Well, h bar k is momentum, so this is more or less p squared over mass, this is the reduced mass, recall this is the reduced mass, more or less the mass of an electron. So what we have on the right hand side is p squared, well it is p squared for k is equal to 1 over A naught, so if you have a wave which has a wavelength which is comparable to 1 over the this scale radius here, sorry a wavelength comparable to this scale radius here, not worrying about 2 pi's at the moment, then what you have on the right here is, so this side is 2 times kinetic energy associated with the particle which has a wavelength which is on the order of A zero, and what we have on the left side here is the electric energy, so the scale that's being set, this dimensional quantity, the Bohr radius, is the natural scale at which the kinetic energy associated with the uncertainty principle, the zero point in it, what with the harmonic oscillator we would have called the zero point motion, is on the order of the electrostatic energy, that's dimensionally where this number comes from, that number comes from. So with the thing to notice now is that Al is dimensionless, why is it dimensionless? Well, this cancels the dimensions of this, obviously this cancels this, this is all dimensionless, this factor apart from the A zero, and here we're looking at, again this is PR divided by, with this put on the bottom, H bar over A zero, therefore H bar K, therefore something with the dimensions of P. So this thing here, this operator here is dimensionless, same as the ladder operators in the harmonic oscillator were dimensionless. Okay, so what do we do with that? What we do is we calculate what A, and this thing of course carries the subscript little l because little l, the orbital quantum number is appearing in its definition, and what we do is we now calculate Al dagger Al. Right, so what does this give us? We have obviously an A zero squared over two out front because we're going to have two A zeroes and root twos, and then we're going to have PR, we showed was a Hermitian, well we engineered that it was a Hermitian operator, so when I take the Hermitian adjoint of what I have up there, I get a minus I PR, the minus sign is from the I over H bar, and then the rest of course is the same because it's Hermitian, well it's just boring numbers, plus Z, well actually this is an operator strictly speaking, but we're in the position representation, so it looks like a number, and that has to be multiplied onto I PR over H bar, so no minus sign because this is Al I'm writing down now, minus l plus one over R plus Z over l plus one A zero, so we have to multiply this stuff out, and the way we do it is we regard this in the back here as one factor, and that in the front is another factor, so this is looking like the product of a number minus some number, a number plus some number, right, the usual pattern, just so this is mirroring very closely what we did with the harmonic oscillator, so we get A zero squared over two, these two obviously multiply together, and we get PR squared over H bar squared, and then these I have to multiply together, so what do we get? We get the square basically of this number here, so we have plus l plus one over R squared plus Z over l plus one A zero squared minus the cross term here which is going to be, well there'll be two minus twice, two Z, those are going to cancel, and we will have A zero R, so that's that's the the two easy parts, right, because it's the front thing squared plus the back thing squared, and now we have to think about the cross terms which would vanish because this is A plus B into A minus B spiritually, these cross terms would vanish if we weren't dealing with operators, and they failed to vanish only because we are dealing with operators, so that there's a failure of commutation, in other words the PR, well okay, so PR commutes with this, so for the cross terms we do, we don't get anything from this thing on this, but we do get something from this thing on this, namely we get the relevant commutator, so the extra term that arises because we're working with operators is going to be I over H bar, that's that, so this minus sign and this minus sign cancel, we have that l plus one and then I have a PR comma one over R, plays big bracket, that's what I'm going to get from this term on this term not canceling on this term, on this term, so that's going, so what is this going to come to? Well let's rearrange things, A0 squared over 2 PR squared over H bar squared plus l plus one squared over R squared minus, I'm going to put this one down next, 2z over A0R, then this term plus z squared over l plus one squared A0 squared, and when I have to do this, what I remember is something we handled already last term, that when I had to do, it arose when I was doing, when we were doing the commutator of P and V, the potential function of X, that turned out to be the rate of dv by dx times the commutator of P and X, this is exactly the situation we have here because this is the operator canonically conjugate to R, so what we have here is the derivative of one over R, which is so minus i l plus one, l plus one over H bar times minus one over R squared because that's the derivative of one over R, times PR comma R, but this is a piece of a canonical commutation relation, this is equal to minus i H bar, right? We show that R comma PR is equal to i H bar, so in this order it's minus i H bar, so we have rather a load of minus signs, let me see, I think we have one, two, three minus signs and another minus sign coming from here, so I think in total we have a plus sign, so this stuff here I believe comes to l plus one over H bar R squared, sorry the H bar cancels, this H bar is on top, that's on the bottom, so we get an l plus one over R squared and this can now be combined with this, except I've got the wrong blinking sign, let me just double check that, yep I'm looking for minus, is it minus? Well anyway I want it to be minus so let's declare it to be minus and I'm sure it is minus, I'm sure it is minus, let's not spend time chasing down some rigid sign because now what we're going to do is combine this, so let's just a little side calculation here, we're going to have l plus one over R squared brackets l plus one from up here, that's the l plus one squared minus one times this stuff, so you can see we're going to put this and this is going to give me an l l plus one, which is exactly what I want, so this is going to be a naught squared over two P R squared over H bar squared plus l l plus one over R squared minus two z over a zero R closed brackets and then I'm going to take this and join it on that so we get plus garbage and the garbage term is z squared over two l plus one squared, this should all be dimensionless, I think it probably is dimensionless on the grounds that it's the product of two dimensionless operators, now what's the point of this ridiculous exercise, the point is that we should see the original Hamiltonians peeking out here, we should basically have our original Hamiltonian plus garbage, so in order to get our original Hamiltonian we need to have a mu under here and a mu under here so why don't we multiply by a mu on the top and the bottom, so this is a naught squared mu and we want to take this H bar outside and then that won't be under there as we want, we can allow that two to wander inside and then this bracket becomes HL, this stuff here becomes HL and we still got unwanted garbage in the back but that's exactly how it worked with the harmonic oscillator, remember a dagger a was equal to H, the Hamiltonian over H bar omega minus a half, there was garbage in the back which in that case was a half, so this is obviously some constant with the dimensions of energy, I better make sure that I've done that right, it's the H bar should be squared, yes of course it should because it was the H bar I took out from there otherwise it is correct and that's just the business, so we've expressed H, let's write this down in the other way, we've said that H is equal to H bar squared over a naught squared mu which must provide the dimensions of energy, a dagger L al minus z squared over 2 L plus 1 squared, another way of writing it, we've expressed H basically as dimensionless constant times as of a dagger a, so this is the harmonic oscillator trick and it's all just looking a little bit messier but this is only a boring number, what's the difference between a half and this, it's just a number, they're both just numbers, rational numbers, okay so what do we do next, what do we do in the harmonic oscillator, we calculated a dagger comma a, we found the commutator, that was the next thing that we did and that's what we do just right now, make sure I'm doing it the right way, no it's more convenient to work it out the other way around, later use, all right so what is that, we have to write this horrible thing down again, so we're going to have an a naught squared over 2, sorry open a square bracket because we're talking commutators now, write down I PR on H bar because I'm writing down a now which is just there, I need to write down minus L plus 1 over R, I don't need to write down the boring constant in the back, the z over L plus 1 a0, that will commute with everything in sight and that will make no contribution to the commutator, then I have to write down the corresponding parts of a dagger which is minus I PR over H bar minus L plus 1 over R and now I can rest easy. So this is what the commutator that I have to do, obviously so PR commutes with itself, nothing doing there, PR on the other hand does not commute with this, so we are going to get a0 squared over 2, I L plus 1, that's that L plus 1 over H bar, that's that H bar PR comma 1 over R commutator, I get that from that, or at least live in hope that I do, what did I do with the minus sign, I put it in the bin, I shouldn't have done, there should be a leading minus sign, then I have the same term actually because here I'm going to get plus, but everything plus this except I'm going to have a 1 over R comma PR, which of course is minus this, so I'm going to get this all over again, so why don't you just rub out the 2 and then it's right. What's this commutator, we've already discussed that problem, it's going to be the rate of change is going to be d by dr of this times the commutator, so this is equal to minus a0 squared I L plus 1 over H bar, and then I'm going to have a minus 1 over R squared for the derivative of this times PR comma R commutator, because that's how these things work, but this once again is minus I H bar, so the 2 minus is here cancel, the 2 I's make another minus sign which kills this minus sign, all being well this is equal to a0 squared L plus 1, the H bars cancel over R squared, check sign, yeah, should have a, no, that's correct, that's correct, good, all right, so we want to express this, remember the commutator doing the harmonic oscillator case, what was this commutator, this commutator was actually a 1, so the bad news is, it's not looking very promising, at this point you think oh no, it's not good, because our commutator is some damn function of R, but we've seen that damn function of R somewhere before up in the Hamiltonian basically, I've lost the Hamiltonian, there it is, so we've got L L plus 1 H bar squared over 2 mu R squared is appearing in the Hamiltonian, so supposing I would take H L plus 1 and from it I would take H L, then everything in the Hamiltonians would cancel except that middle term which has the right form, namely it contains a 1 over R squared and what would we have, we'd have H bar squared over 2 mu I think, R squared brackets L plus 1, L plus 2 minus L L plus 1, did I do that right, living home, okay, so obviously there's going to be a factor of L plus 1 common and then we're looking at the difference between L plus 2 and L in other words 2, the 2 is going to cancel this and this is going to equal L plus 1 H bar squared over mu R squared, so we can express with this little side calculation we can go back up the board and express this as an appropriate multiple of the differences in the Hamiltonians, there's going to be a naught squared, that's this a naught squared, then we will want to multiply by mu divided by H bar squared and then we'll be able to say these H L plus 1 minus H L, check that we haven't got any horrible factors in this, all right, what was the next thing we did in the harmonic oscillator, having got the commutator of the A and the A dagger and having expressed H as a product of A and A dagger, the next thing we did was calculate the commutator, use these results to calculate the commutator of A with H, so that's what we do now, I will do it here so that we can see our results, so I want to calculate the commutator A L comma H L and I can do that by expressing this H L, you see H L is basically a product of the A's, now I've only got to locate the retrofit product, it's at the top there isn't it, it's so hard from this position to see what you need to see, this product, et cetera, et cetera, there's a statement, this is a statement I'm looking for, I want that statement, all right, so this H L can be traded in for that product, so we have H bar squared over A zero squared mu times the commutator of A L and A L, A L dagger A L and I can rest easy there, I no need to put this stuff inside a commutator because it commutes with everything inside so it can't contribute to the commutator, so this is the commutator I have to evaluate and this is easy because this is a commutator of product, some A with B and C which in principle is the commutator of A with B C standing idly by and then the commutator of A with C B standing idly by but A of course commutes with itself so there's only one term which is an A L, A L commutator with A L dagger, so this is equal to H bar squared over A zero squared mu A L comma A L dagger and we just work that one out and the answer was, and the answer was, it was here, sorry I did something wrong, yes it's very important, I need an extra factor A L, thank you very much in the back, this is standing idly by while A L works on his companion, all right, so I now need to plug this in for this commutator and you can see that all these factors are going to cancel, this factor is going to cancel on this factor and so we're simply going to get H L plus 1 minus H L times the A L I've been very helpfully told to include so let me just, right, so we're now in wonderful shape, so we've completed all three steps of the simple amount of oscillator calculation and now we just need to go for the point of the exercise which is, so we're given that we always were given that H L on E and L is equal to E of E and L, right, what we want to do is make ourselves a new, so we've got one stationary state, we want to make ourselves a new stationary state by multiplying by A L, obviously both sides of the equation, so let me write down the right side of the equation first, this implies that E, which is a boring number, times A L, E and L is equal to A L, H L of E and L, usual business, swap these over, H L, A L which I'm not entitled to plus the commutator that restores order on E and L, we just worked that out and found that it was the difference of two H's times A L, so this becomes H L plus 1 minus H L with an A L in back, guess what? We have an H L, A L here with a minus sign and H L, A L here with a plus sign, so the whole thing is equal to H L plus 1, A L, E and L, so we have achieved what we wanted to achieve, that is to say we have shown that this state is an eigenstate, not of H L, but of H L plus 1 and for the same energy, so the map's looking a little different now from harmonic oscillator, but nonetheless we have a very powerful result, we have generated ourselves from a state which had energy E in angular momentum quantum number L, we've made ourselves a state which can only be characterized as E L plus 1, we've made ourselves a state of the same energy but more angular momentum, so what have we done? This operator, this is some normalizing constant, right? We had just this kind of thing in the case of the harmonic oscillator, so physically what have we done? Well, classically what have we done? We've taken an orbit that might look like this and we've turned it into an orbit, I'm trying to make an orbit that has about the same semi-major axis and is rounder, you know about Kepler orbits, so with the same supply of energy, we've increased the angular momentum so we've made the orbit less eccentric. So in the several-line harmonic oscillator case, what did we do? We made ourselves an orbit with less energy and then we argued that the energy we were able to show that the energy could never be negative, so we said to ourselves so there must be some, so given this state now, we could apply a l plus one, a sub l plus one to this and make ourselves e comma l plus two, state with even more angular momentum, so like in the harmonic oscillator case, we said we could make ourselves an orbit with even less energy. Is this possible with a given supply of energy with a bound orbit to have more and more and more angular momentum? No, it's not. At some point, you've got the maximum angular momentum you can have for that given energy, which in classical physics is what we would call a circular orbit. We've completely destroyed the radial motion. See, what we've been doing here is we've been shifting kinetic energy. We've shifted ke from pr squared over two mu to l squared h bar squared over two mu r squared. This was the tangential kinetic energy. This was the radial kinetic energy. We've shifted energy from here to here. When we've got no energy left in there or as little as the theory as quantum mechanics allows, which won't be zero, but will be some amount, then we won't be able to shift any more. So there must be a maximum angular momentum for a given energy. We'll call this curly l. This is the maximum angular momentum and it is a function of energy, but we won't write that it's a function of energy. But we're gonna find out what function of energy it is. So what does that mean? That means if we take the, if we take the, what are we gonna call this, the circularization operator, AL, belonging to this maximum angular momentum and we use it on the state which has the maximum angular momentum for the given energy, what do we get? Nothing. That's the only way we can be prevented from getting a state which has even more angular momentum for the same energy is if this operator simply kills this state. So we've used this argument twice before, once in the harmonic oscillator case and also in the case of the angular momentum operators. What do we mean by nothing? What we mean is the mod square of this is nothing. What does that map to? That maps to e maximum angular momentum, AL dagger AL, e curly thingy is not. Where have we seen a dagger a before? I think we must have seen it in the Hamiltonian. We need to replace that by the Hamiltonian times some horrible factors. Yeah. All right, so we, well, we already have it here. So a dagger a comes right down to this line here. So this line here can replace the a dagger a in here. So we get to have that e curly L onto a naught squared mu over h bar squared h curly L plus z squared over two curly L plus one squared closer bracket e curly L, ain't much. But this thing, this is an eigenfunction of this operator with eigenvalue e. This is a boring number. So it stands by whilst this bangs into that and makes a one. This gives me e times this and this is left over and it bangs into this and makes a one. So this implies that a zero squared mu over h bar squared e plus z squared over two L plus one squared is nothing or perhaps I should write this as equals minus. So what have we done? We've got a relationship between the energy and the maximum allowed angular momentum. More than that, we know that these angular momentum quantum numbers, because this is orbital angular momentum we're talking about, we prove that those had to be integers. So n being defined to be is an integer, integer. What integer? We know that curly L is allowed to be nothing one, two, three, four. So n is equal to the numbers it's allowed to be is one, two, three, four, blah, blah. Nothing not included in the list because of that plus one. So we have shown that e, the energy, has to be of the form minus z squared h bar squared over a naught mu, we've done that right, a naught squared mu one over, no we need a two here, one over n squared. So we have found the possible energies of a hydrogen atom. Well, in fact, for a hydrogen like ion, because z remembers this integer, which controls the number of charge units on the nucleus, we have found this with the possible values, right? It's given by this constant, which we know what it is. We'll simplify it in a moment, we know what it is times one over n squared, where n is one, two, three, four. So this gives the energy levels. We write this as minus z squared times r, over n squared, where curly r is whatever you see it to be, which is h bar squared over two a naught squared mu, which is not very intuitive. The way to make this intuitive is to take those a zeros, there are two of them and turn one of them back into its h bars and things. Now, where did we define a zero for heaven's sake? It was right over here somewhere, right? There it is.  So this is going to become, on the bottom we're gonna have an eight pi epsilon naught a zero, all right? That's the four pi epsilon naught. The h bar squared will cancel top and bottom, so that goes away. The mu and the e squared, well the mu will go away with this and the e squared will sit on the top. So the Rydberg is what? E squared over four pi epsilon naught a zero would be the potential energy of two charges of charge, you know, two electric charges that were separated by a zero. So this is half of the potential energy at a separation of a zero. And so this is the fundamental energy scale of atoms. And what is it equal to? 13.6 electron volts plus, you know, 13.6 to three significant figures. So the energy range at which we work, you know, the battery that you stick into your, you stick into your camera or something has 1.5 volts basically because of that 13.6 EVs. It's all of, all of condensed matter physics is a mere reflection of the energy. Condensed matter physics is a mere reflection of that number. Rather, you know, this is why we live at one EV not at one MEV or one millievery or whatever. So what do we need to do next? Yeah, jargon. This is called the principle, principle, pal, AL, quantum number. So in these hydrogen like ions we've discovered that there are a whole series of different, of distinct states which have the same energy and different angular momenta. So let's talk a bit about degeneracy. Okay, so for principle quantum number n equals one, we have that L, which is equal to n minus one is equal to zero. And almost the largest angular momentum you can have is nothing. And in the ground state of hydrogen, there's one electron, it sits in the state with the lowest energy which is going to be associated with n equals one and it has no angular momentum. It's on a totally radial orbit in classical physics, right? Not going round and round at all. It just goes in and out, in and out. I mean in classical physics, quantum mechanics. But it doesn't have any angular momentum. So that's a surprising result. For n equals two, L is equal, the maximum angular momentum is equal to one. That means that L can be naught if you like and L can be one, right? This is the maximum angular momentum. So there's a slightly funny thing going on here. n was introduced as one plus the maximum angular momentum. But now I'm saying it's better to what we one standardly thinks about it. One thinks about what's the value of n from it? One takes as n minus one the maximum angular momentum. So, sorry. And in this sense, we have one state. It'll be two states, well, there's one. Here, basically we have, this is for a spinless particle, right? It'll turn out to be two states when we include the spin of the electron. But remember, we were doing the growth structure which means we said we were gonna forget about the spin of the electron. Here, we would have one state and here we would have three states, right? Because for L equals one, we got total angular momentum one which means we got three possible orientations of it. m can be one, nothing or minus one. So we have three quantum states here, one here. So we got four states all with the same energy for n equals two, one for n equals one and so it goes down the line. So the number of states is increasing rapidly because there'll be five states for n equals three. The maximum angular momentum will be two. For two units of angular momentum, you've got five possible orientations and then you've still got three of these and one of those, so that's nine states, et cetera. So the structure we've derived is extremely degenerate. What does this have to say about experiments? So stick some hydrogen atoms in a vessel and pass an electric current through and get the electrons knocked out of their comfortable, out of their comfort zone and you will get photons coming out at discrete frequencies. Nu is going to be the difference in the energies over H which is going to be z squared, the Rydberg constant over H, over H null H bar, one over n prime squared minus one over n squared. This is for n goes to n prime. So if you were in one of these higher states, for example, n equals two, you will have less, your energy will be a smaller negative number, right? You'll have one over two squared, you'll have a quarter here and this could then fall down to the state n prime equals one, in which case this will be one, so this bracket will be, say, three quarters and you will get three quarters of this number coming out. So that gives you some frequency and what we have is series of lines. So the way we think about this is that we have a series of lines each for fixed n primed, i.e. bottom level. So if we fix n primed at one, we can have transitions from n is two to one or n is three to one or n is four to one and these are the successive lines of the Lyman series. So here we have, so here is the energy of n equals one, here's n equals two, here's n equals three and Lyman alpha is the name used for the spectral line associated with an electron tumbling from n equals two down to n equals one and Lyman beta is associated with from n equals three down to n equals one, which is further to four so it emits more energy so the line appears at higher frequency, longer, shorter wavelength. So the Lyman series is for n primed equals one, if n equals two we're looking at Lyman alpha, that's what it's conventionally called, if n equals three it's Lyman beta and this has I think it's 112 nanometers, is that right? 121, sorry. And as you go down to n equals infinity, in other words, if you fall all away from not being bound into the bottom of the atom, then this is the beginning of the Lyman continuum and that's what is it, 92 nanometers roughly speaking, I've got a more accurate number here, 91.2. So these lines are all in the, these are all vacuum ultraviolet lines, they all carry, so this one is carrying 13.6 EV of energy and these are carrying, this is carrying three quarters of 13.6 EV of energy, so they're carrying enough energy to kick electrons out of the air molecules so these photons are heavily, are absorbed by all kinds of things, they're very, these are very easily absorbed photons because they carry enough energy to lift electrons out of most atoms. And then we have the next is the Balmer series, which is where the whole story started, which is so n primed is two, n equals three, if you go from three to two, that's called Balmer alpha, but it's written as H alpha because that stands for hydrogen alpha, so Balmer was a Swiss school teacher who empirically fitted the formula and we've derived, I've lost it, there it is, he fitted that formula empirically to measured frequencies of lines that he identified as being the Balmer series lines, well, A series of lines, he called the hydrogen series, so this is called H alpha and it's a pink photon, it's 600 and something nanometers, 656. So it's pink light. So many astronomical objects are pink because they are shining in, sorry, in H alpha, in Balmer alpha, this is H beta, et cetera. If you, then you go to passion, that's for n primed is three and obviously n can be four or five, et cetera, et cetera, et cetera.  So they go from pink light right through the optical, the rest of the optical spectrum to the ultraviolet region and the passion series starts at 1875, I think. So n equals four, you are looking at 18, yep. So that's already, these are sort of more or less optical and by now we're in the near infrared, et cetera, et cetera, et cetera. So that's pretty much the right place to stop, I think. What we should do, just one other thing I would point out is that, so you can apply these formally to the inner electrons of, to the innermost electrons of other atoms, atoms that have more than one electron, you can't apply them to the outer electrons with any useful way because we've done all this right, remember with no other electrons present, we got one nucleus and one electron, but there's one very important thing to take home, which is that this energy scale goes like Z squared. So the energies, the characteristic energies of the innermost electrons are going up like Z squared by the time you get to uranium, which has 92 units of charge, so Z is 92, you're almost a factor of 10 to the four, you're almost a factor of 10,000 higher in energy, which means that these electrons are moving essentially relativistically. So that's just the thing to bear in mind. Okay, and we'll look at the wave functions that go with this lot tomorrow.