This now I'll record it on my computer and then upload well. I'm not sure I have not done this before, but there may be a bandwidth problem if I'm doing it otherwise.

Good.

So what do I want to do first? Well, I have told you already that this week is unusual, so the very first lecture I just want to make you aware of all the different technicalities and how we run this course online.

So we will run this course online of course through canvas and all of you should have this canvas page if you try to go to vital. There was an announcement that everything would be on canvas and that's it. For valuable I will refrain from using it for anything cause I think overlapping a virtual learning environments would be plainly confusing.

So everything should appear on canvas basically, but the scheduling of the meetings will be hopefully through your timetable, but also for things that I'm doing at talk, like like possible one to one meetings like office hours like possible additional revision sessions later on, or some feedback sessions. All these things I may just have to give you the links through canvas and then you can click at them and join.

A meeting with me.

Or with a larger class.

So what what I want to do now is I want to share my screen, but first I need to be sure I'm bringing right up the the right window.

Too many windows on my machine, so I'm working with various screens in order to have a bit more control. But this means sometimes it's more confusing for myself.

So I'm there are plenty of options in these zoom meetings, so if something is not working, bear with me. I tell me give me a shout in the chat or or in or with your voice and muting your mic and then because things may look different for me then they look for you so I do it now a.

I do know screen sharing you shouldn't be able to do a screen sharing but but I can so I'm clicking at 1:00 particular window to share one particular screen and this screen that you should see. Now is a window from a browser, which I'm using which is actually not the recommended one, but it works seems to work and I'm showing the mark 325 canvas module.

As you would see it and I would see something different and I just want instead of having separate slides for all the announcements walk you through what is already there. Sorry if you have seen this already, but at the same time just signposting you where to get this information and making the announcements now and having it in the recording will help lay join us and also help you as a reference point and so as an introduction now so.

Confusingly, I must admit, but this is outside our control canvas talks about modules when when they mean just subsections in a course and our what we call module is Mar 325. This is called cost in canvas, so try to avoid confusion there, but we can't because we can't redesign canvas. It's a big international product.

That this rollout in many institutions?

So in modules there are things like cost information, lecture notes and problem sheets, and they will appear more things as we need them like material for revision, like extra examples like solutions to problems like maybe extra material which is not included in the lecture notes etc. As we go along, this will be populated further, but the important thing is now that we have something like a study plan, so I'm clicking at it. It's a bit slow.

So we have a study plan here and I.

The study plan is different from normal, so normally we would have three lectures and one tutorial and now we don't have the lectures anymore. So site remark here. So the face to face lectures half as you're probably fully aware by now, had to be cancelled because the infection rates in Liverpool are just too big.

And we had originally planned to give every student on our program 3 hours face to face, so that would have been a bit like the lecture hours, but organized in a slightly different way.

And then there is the one hour which we have now, which may be considered like a tutorial, but may be used in a slightly different way as today. Depending on the week.

So the IT may be that 'cause we can't do the face to face like trust, we will try to provide some version of it online, or we may revert to having more sessions for individual modules.

We do not know yet how what we are, what we can do, what we will do. It is very tricky to change time typing on the fly, but there are things happening in the background, so bear with us for the time being. We will have the one session, the one online session that is dedicated entirely to my three to five per week.

But there is more to it. So what you should do. Your study plan is attended tutorial which is right now. And I say tutorial when it's called on if it's called online session tutorial today it's more a lecture.

And typically I will try to give additional explanations. Short wrap ups of of something that is needed to solve problems. Discuss problems where you instructed with it. Let you 2 problems like you ask questions and try to make this as interactive as it can be using now our online mode.

So the most important thing is that you work.

As continuously as you can through the various chapters. So there is a detailed lecture notes fully latex and with pictures are of course available already and there is down there on the screen. There is no the plan what will be covered in each week, so I have we have 12 weeks in total but not all of it will be needed for covering the material. I hope they will in the end be revision and there is some additional material.

In Week 11, which is not in the lecture notes, Maybe I will come conclude it in included in the lecture notes in the past I made this with a slightly different style. Have to see how it works online. So for example in big one you are not just the chapters to map 1 to one to the weeks that would have been rather artificial. So in big one we will cover you should cover, you should read and really carefully study, possibly with other sources, chapters one and 2.1.

Of the notes and then there will be a problem sheet.

And there will always be a problem sheet in each week there will be a problem sheet apart from week nine when there will be an assessment more about this in the moment. So the plan here is really go along here.

Do really the work if you don't understand something, try other sources.

Discuss, ask me come to office hours so these are additional hours where we then can really have interactions.

So it is.

The online tutorial working through the specified chapters doing the problem sheet. Now the problem sheet I called problem sheet and not homework 'cause they well, everything seems to be from home right now.

So.

It does not count to your module mark, but you can handle him. So I will open an assessment link where you can upload it. So as we same way as we have done on vital you can work things out. On paper. You can of course typeset solutions, but that would be considered an overkill and then scan in one portrait PDF file so that we can easily download and annotate it and then you will get.

Individual feedback on this.

And that you, if you don't want to have this, if you think it's not needed, that's absolutely fine by me. But it is important that you were continuously through the problems cause learning quantum mechanics. It's not by listening or reading only. That's very important, but that's not all we need to be able to solve problems, because only then it becomes clear where the nontrivial points in the formalism are, where the technicalities lie, when it comes to the method.

And pure maths of course that sits behind.

So what you can, what you can then do is, as I said, upload them. Typically I want to have this on a Friday so that in the tutorial the week after in the next week there is already some feedback possible. Hopefully at least I can look into it and I may then discuss some of the problems that have occurred.

Close in time to when you worked on it.

So there will also be recordings each week, so this causes lecture notes based, so I'm not trying to give you.

Very lengthy recordings which are very painful to listen through. Typically it's not as interactive as in a lecture. It's harder for me to speak into the void of a screen with the microphone and camera attached to it, but what I will do, I will make each week. There will be a shortish recording, the minimum that you should get is 20 minutes, but that may not be enough for me. So let's let's try out how it works and I will summarize the main points covered in the given League.

This should not be your shortcut. Just watch through this and that's it. You should really study the lecture notes, maybe make your own notes or annotate what you have there, but work basically with this and then with the active learning mode tutorial sessions. So lots of words. I'm not sure how they will really work out. In the end it a lot will depend on you and how you can actually participate. How actively you can participate technically, but also time wise.

So these recordings will more be as a something like a recap and possibly good for revision. Possibly good for you to check your understanding or of course as a sort of mini summary if in a week you for whatever reason couldn't work the hours required to go slowly through the notes, I would also really encourage you to take books out of the library to study.

Possibly with online resources alot nowadays when you're not sure about a math problem, Lotis on things like Wikipedia. Of course there are youtubers who are much better in setting up lectures online lectures than I am, so you may find something that is good there, but I will give you short recordings. So far none has appeared 'cause I haven't published any yet because I want you to really start working with the nodes.

So that is this study plan here, week by week, and it may be subject to small changes, so bear with me. Don't don't print out everything. That's also true for the nodes. I'm not doing this quantum mechanics course for the first year. It's a third here. I'm doing it so a lot of typos have already been found and corrected, but there are still things that I want to change. So if you.

Download and print out everything that that's OK, but maybe there will be slight changes later and then referencing to page numbers will not be helpful, but the equation numbers and chapter numbers and things like this will stay. So that is the 1st that is the first page that is in in this study plan here. So now I'm just trying to chuckle my various windows here.

So I tried to go back so there is homework. I have already said that in words, so here I say it again, but there will be then on this page there will appear a link where you can really see where you can really then upload your things. I still have to work out exactly how to do this best in canvas, but it will be very similar to what you're used to in vital.

So there should be a next button somewhere there hidden behind another window, which I'm not sure if you are seeing. It's just my control window for this.

For this session. So then there is assessment, and that's always something that comes up. How is the assessment like? And it's not as you used to be.

To have it, it's not as it used to be. It's not as you used to have it, so there will now be 2 assessments and they will both wait exactly 50% to the module mark. So it's like 2 mini exams but one will be at the very end in the exam period as usual and the other one will be. It's not really a midterm exam becausw the timetabling and the scheduling of all the various tests and exams that you will have that they don't allow me that, so it's now it's.

Probably it's planned to be in the teaching week nine. That's the that's right. Before that is, pretty soon before the Christmas break, so by that we will already have covered enough material. I wanted to have it earlier, I should say, but that's not doesn't look possible. Now we'll have to see.

So timetabling is still in the in a flow. That's unfortunate, but cannot be avoided, because everything in these days is a bit in the flow.

So if I just click it next, that is an office hours and for this week I have scheduled Wednesday 11 and Friday 10. How? Why? These times? Well, you you may say, but I can't. I have something else. The problem is in a class of 40 something students from various programs. There is so much overlap in the timetable that I haven't found good slots and doing slots very early or very late would not be good. 'cause some of you couldn't and wouldn't want to attend either, especially.

If some of you are still overseas, then late afternoon slots would be would be horrible. They were in the middle of the night.

So that's office hours and I will. I will bring up links I'm not sure yet if I'm doing this with zoom. If it all works fine, teams is better integrated with file sharing in our in our University of Liverpool file spaces. So I.

I'll come up with something so that by Wednesday you just have a link that you can click at.

So now the next module here is the lecture notes and the lecture notes you probably this was the first thing that I have put up, so you can. You will probably have looked at them. One can scroll through it, that's a bit slow in this in screen reviewing. Of course you can download the whole thing and you can then basically, well, you can do whatever you want with it. If you have a tablet.

Or if you do this even on your mobile phone with a touch screen, you can annotate them. You can of course print out and hand annotate like sometimes like to work on paper, not the whole day on the screen, but of course it is easy to share something that is electronically available, so I will use annotation using a tablet during this course for sure. So these are notes with long list of tables and figures.

By this scroll is terribly slow on this green, so will we will come to this later and basically this will be your main source.

So now the next little module for which there is information there. That is the problem sheet one.

And the problem sheet one is very basic.

And if you find it trivial, then still remind yourself about what what this is all about. But most of you may not find this completely trivial and the underlying linear algebra, the matrix operations, they are really important to master the actual calculations in quantum mechanics. The first question here will be about the so called Pauli Matrices, which have very specific properties and these properties and they play a very important role in quantum mechanics.

And there will be general properties of matrices and there is a matrix given here now, not with numbers, but just with the variable F, but only specific matrix elements. Here entries are populated with this F, the others are zero and then you should workout the eigenvectors and see that there really orthogonal and then really understand the properties of specific matrices that are so important in quantum mechanics.

And this is a sort of recap of linear algebra and the last question here will then talk about an object which we will start to introduce well is introduced soon in the lecture notes coming up rather early, and this is an object that's called the commutator and the commutator. And we're just using the square brackets, and then there is something like a matrix, a combimatrix be square bracket closed, so this commutator is defined as the product AB.

Minus the reverse ordering of the two operators or the two matrices, I'm dropping a lot of words here already, but don't worry if you read slowly through the nodes, that should all become very clear very soon.

And then you should prove specific relations, which are called commutation relations between the Pauli Matrices Sigma, one Sigma two and Sigma three that have been introduced.

In the problem one.

So let's see very specific properties which actually go beyond the particular representation of these matrices. But this is very specifics which I don't want to bother you at this point in time, so there will be. We will make use of an index notation. There is a Sigma I buy runs 123, so this is means even though the Sigma is a matrix, there are three of them, so if you would want to depict individual matrix elements with indices, you would have to choose different symbols and maybe put them.

Toppin, but as a subscript.

So that's the material and the advice that is out there for the moment and.

So I returned to the main screen, so there are these three modules cause information, lecture notes, problem sheets. And as I told you they will appear more importantly on the left side. Here there are things like announcement. I have made announcements you can control in settings how these announcements work for you, how often you get emails. I don't want to overwhelm you, but I can't really do that. If you restric how much you get and something should end up in your email I guess.

To be sure, you you get every two you get alerts. If you're not constantly on canvas, but maybe you are now.

Then there will be discussions. It will be very important for me that you don't be couple, but that you fully engaged and for this having things like the office hour office hours or using the discussion board and possibly emailing me this will be main modes of interaction. So the discussion I always try to encourage using discussions 'cause then others can see it as well and it's much better and much more efficient. Having a discussion with several people so you may help each other you made.

Instead of me doing just individual emails.

And then there will be. There will be things like file space and there is a syllabus. Actually I think I have put something in the syllabus and what I have put in the syllabus is basically the contents page of the lecture notes.

So you can see here how this Maps on on what is sort of the syllabus from the module as it would appear in the module specifications and as announced on web pages. So we have an introduction we have to start with the general Thierry. Very important there are the so-called postulates of quantum mechanics. You cannot derive quantum mechanics as such from from classical mechanics. You can do it the other way around, but you cannot do this way around. So we must postulate somethings.

Like in Newtonian mechanics, when we have certain laws which we assume and certain framework. So there are postulates of quantum mechanics and then we will basically build the apparatus to solve simple time dependent and time independent problems. And this is a big chapter, so it definitely goes beyond the two.

And then we will talk more about the formalism in terms of operators and their commutators, and they have just already shown you this.

Before the commutator and which comes up on the 1st sheet. And there will be things that you may have heard about Heisenberg's uncertainty principle, gaussian wavefunctions, wavepackets. Then we have the simple harmonic oscillator, harmonic oscillator plays of course a huge role in classical mechanics and in related fields. But it's also very important in quantum mechanics and beyond.

And then we will move from one dimension to more dimensions and then we will have to introduce as we have done in math 122 in mechanics and we will have to introduce the angular momentum. But now in the quantum mechanical version of it.

And in the end, towards the end of the course we will find methods we will define and explore methods which we can use to approximately solve problems cause a lot of real world problems could never be solved in full generality, but you have to make certain approximations and use certain techniques and two of them will be covered. Variational in perturbation theory.

And then we will talk about a particle in a central potential becausw. This will really lead to one of the most beautiful.

Discoveries in the way that the mechanics in quantum mechanics explain atomic physics, and so the hydrogen Atom, the simplest Atom that we have. We will be able to calculate in quite some detail and in the end there is a chapter still without content with interpretation of quantum mechanics and paradox are and.

I this will be in the very end and we'll see what in which way we can cover. This is not something that will be part or that is planned to become part of an exam.

So this is Silipo center. Then there are many more ways to collaborate here. Most of them are not using in the moment, but what will be?

Fuse of course, is the stream lectures were lectures will come up this recorded lecture, but also lectures which I will do this weekly recap and summary lectures, which I will put in this space. So that's a slow walk through and that everybody is hopefully on the same canvas page.

What I want to do now for a moment is I stop sharing my screen.

So I'm back to a big control windows or staring at the big screen. This is when I'm looking up because the camera is down the laptop which I'm using to type and have have other windows open.

So.

What I want to do now is I want to give you a short introduction in very general terms, but before that I tried to start.

A little polling I. Let's see what I can do here.



I have not done this before.

So type your question here. I want to know are you in.

Liverpool.

Or

her.

Not in the area area abroad and.

So.

Are you in Liverpool or why? OK, I shouldn't have done this in real time. Now you are seeing the the pitfalls here because you don't see what I'm doing. You're probably you're probably asking yourself what is he doing? I'm trying to design A pole here.



And I'm making this anonymous because I don't want to have a lot of.

Personal.

I'm, I'm afraid this doesn't really work. I have to train this first and to figure out how it works.

So what I want to do, I want to use polling and I haven't done this.

I haven't done this before.

So I'm too slow to do it in real time. I thought it would be more obvious.

I'm trying to launch a poll.

But it's not working for me for whatever reason, and actually now certain screens are freezing. OK, so forget about this what?

I can still ask the question.

And look at my screen. If you give me the just the thumbs up or the thumbs down so everybody in the zoom meeting control screen there is reactions.

And you can.

Clap, you don't need to clap now, but you can just use thumbs up. So who of the 32 of you who are join have joined today? Who is currently in Liverpool or very close by?

OK, so that is that is actually not not the majority, just as a crosscheck. So everybody who had fingers who had come back take the thumb down again.

How does that work? I you can put it up and put it down again. So who is overseas? Most probably China.

Come up now please so that I can see what is happening.

When it comes to scheduling office hours, for example, this is quite an important information for me. So if you are listening from China late afternoon or or evening now, then then please put up now with the reaction sign on the screen and then.

I can see what is happening here.

OK, so it seems that not so many people are really far away, so a lot of you can maybe quite a few may still be in UK but not in Liverpool, which would be understandable if there is no no face to face teaching right now.

OK, that was a trial and error so I have to workout powers first on my own. Sorry sorry for that but I got the major information that that I want it this way. So what I will do now is I will first bring up a window on my screen if I.

Can

and then share this particular window with you to give you a very general introduction.

Inverts not yet formulated about quantum mechanics, so I will again.

River to the screen share mode.

And.

OK, I'm just sharing now my little introductory set of slides.

So.

You may ask yourself what is so special about quantum mechanics, and I hope that after reading the week one material you will be able to answer this to some extent already. Maybe you know already know, but this I don't know. I don't know who had what caused elsewhere before and how much you started at school.

So for me, together with Einstein's relativity, quantum mechanics is really so important, because historically it means that.

It was a break away from classical physics, so before that there was a lot of good physics done. A lot of understanding of what happens in nature.

But there came a point when the existing concepts in classical mechanics and you told and mechanics in fluid dynamics and electrodynamics when there were just not enough to understand the world anymore.

So in a way, quantum mechanics and I should say together with Einstein's relativity, they started a new era in our understanding of nature, and the history is not not that long ago.

So with it we can understand this up atomic world.

But even if you're not interested in Atomic Physics in a way, the consequences are really far reaching.

Without quantum mechanics, we wouldn't be here.

Why can I make this statement? Well, obviously quantum mechanics, no, maybe not, obviously, but we will get there in the end. So understated this before and it's how it historically developed.

With quantum mechanics we understand.



We understand atomic physics.

And Atomic Physics is of course at the foundations of.

What makes a meter?

Matter would look different if quantum mechanics.

Wouldn't work.

So.

To which extend you talk about nature being nature, and our Thierry being a description of it and to which extent you believe that the description is actually the real thing. That is a philosophical question. We don't have to touch a pioneer, but basically the way we understand this description of nature here, this detailed formalism has probably some deep mathematical truths inside which really map very well in nature becausw. These atomic physics measurements that have led to.

The development of quantum mechanics or the discovery of quantum mechanics. They are so precise and so detailed and permeate so many, so many areas of our world that.

That they are really at the the foundation of everything. So without these atoms there would be no molecules and without molecules certainly we wouldn't exist.

So, so this comes from the microscopic, but builds up to larger, larger objects which then cannot be described directly in quantum mechanics, cause quantum mechanics is really designed to describe few bodies, and then it gets just too complicated to describe very many bodies when other properties become very important. But at the bottom of it, it's still the description of the of the building blocks.

Of matter, which is wouldn't would not work at all would be fundamentally flawed.

Trying to describe it without quantum mechanics, just based on mechanics and electrodynamics doesn't work at all.

So.

It's only about 100 years old, so a lot of mathematics we are studying is is older.

But it still.

You may say 100 years is a lot, and of course in terms of generations it is a lot. And still after this time and everything covered in Zillions of textbooks, it's considered somewhat mysterious by many. Sometimes you hear people saying that nobody by the very few people can understand quantum mechanics or nobody ever understands it, and the same is the same sort of statements are made for relativity. I don't think that these statements do the subject justice. We definitely can learn it.

So a lot at the basis of quantum mechanics and the same is true for relativity. There are conceptual novelty's and they are hard to overcome if you are trying to understand them.

Within your own classical experience, classical meaning that our world looked at the big scale seems to function very well with Newtonian mechanics and.

A bit of electrodynamics and a bit of Chemistry.

We don't have to go deep into the building blocks of matter and into quantum physics, so we don't have a direct everyday hands down experience of quantum effects.

But

this doesn't mean they are in real, and if you if you do not to some extent, except that these things are there and always try to go back to your classical understanding that has developed over from being from growing up as a baby, handling things and how they work and what they do and what they don't. If you don't give to some extent these preconceptions up.

And you say and are open that there can things that are really different from this. Then the understanding becomes really hard.

So in this respect, B Bond quantum mechanics goes really beyond our classical understanding, but as I said before, this does not mean that we couldn't understand it. So in this course, well, I'm making loads of words here, but I want to sort of start thinking in the discussion, but I should note that in this course we will mostly avoid to get trapped in these philosophical discussions.

So why? Well it may be an interesting subject, but first before you can have a meaningful in depth discussion, you should be able to master the subject to some extent. So we want really to provide you here with the mathematical framework.

With the methods to solve simple quantum mechanical problems.

And most of this will be possible on paper, but in the real world, when you're doing quantum chemistry or solving more complicated systems than the computer is of course the tool that we need to use.

So at the end of the 'cause there will be this this Chapter 7 which has not yet any content in the lecture notes. We will talk about paradox of quantum mechanics and possible interpretations, but this is not the stuff that in a maths cause. I want to concentrate on, and certainly as I said before, this should not form part of, at least not a major part at all of any assessment.

So what are such new concepts? So if you have never had.

Quantum mechanics or atomic physics before, if this is completely new to you, don't worry, it will become much clearer very soon.

But quick recap, sort of. What are the keywords here so particles can behave like waves and waves can behave like particles that comes under the word wave particle duality and the first chapter that you should work through of the notes that you should work through in this week. This really explains how experimentally without going into the great details of the experiments but sort of sketching, what happens. What happens when people try to describe?

Things they started understanding light and they started understanding having having sort of single particles like Electrons and making experiments with them. And then they they understood at some point that well, the particle is not always just behaving like a particle, but we need the description of a wave in order to understand its behavior.

So I think a lot started with that.

But when we are looking at the mathematical framework, the functions which will be used to describe a system.

They will be called wavefunctions, even that is not the only way to formulate things, but we will use mostly BAE functions. They do not relate directly to observable quantities such as the position and velocity of a particle X of T or V of T. As we have done in Newtonian mechanics and elsewhere.

Instead, they will only form the objects which allow for a probabilistic interpretation, and this is the next thing highlighted in blue here. So this probabilistic interpretation is something that.

People off, including Einstein historically because they thought it's not possible that we don't have equations that just determine what is there, must be some inner workings that allows this. And we're just not smart enough to discover it to unearth it, to describe it, and by now we have understood that this probabilistic interpretation is really at the core of quantum mechanics and the core of what we need in order to describe what we see.

So.

Another key feature of which is knew which is not the case in classical physics, is in classical physics. We coupled the object that we that we want to describe from the measurement. We just assume that if there is a body which moves in space, then we may just use a laser laser distance meter to measure its position and that should not change its path.

And that is not true. You cannot, in general, completely decouple even theoretically and Conceptually.

The object you measure from the measurement process or from the observer.

So observe or maybe a machine that makes a recording of something doesn't have to be a human being, but or an animal or a living living thing, but it is something that does something.

Something can be a small change, and when we're looking at the atomic world.

The small change conceptually cannot make cannot can never be made zero change and quantum mechanics will really formalize this. So we end up due to this, which will be then coined Heisenberg's uncertainty principle. We end up with an intrinsic uncertainty in the accuracy will count. One can achieve measuring observable simulataneously.

That's already all the words that will later be.

At each individual word here, measuring observed will simultaneously each of them will become important to really understand the formalism and how it's used to describe. But for the time being just taken that.

If this is completely new to you.

That

There.

There are these funny things that we need a probabilistic interpretation of an object which is of a function. Even though the wavefunction can be perfectly calculated with equations that we will introduce.

But then when it comes to making sense of what these functions and their time dependence tells us, we need to come up with a probability probabilistic interpretation. This is something that that is really conceptually difficult to swallow sometimes.

And this intrinsic uncertainty also.

Difficult to swallow sometimes, but the evidence that the formalism and its predictions work on an incredible level of precision for us, this evidence is so overwhelming and Becausw no work around these probabilistic interpretations and the uncertainty have ever been developed, which really are satisfying and give the same predictions. Therefore, we must assume that this is it for the time being, 'cause you can have the philosophical.

Discussion, but as I said, that is not what we are concentrating on in this course.

So what's the solar quiz? So the solar boosts? Well, apart from the detailed syllabus that goes along with the lecture notes, is really making sense of the wave particle duality, introducing the Schroedinger equation for simple 1 dimensional systems, the equation that governs the evolution, the description that derivation that gives the derivation of the Bay function for a different system. Then we'll talk about how we can use also matrix mechanics to describe.

Things which have finite numbers of degrees of freedom. So a function of X has infinitely many degrees of freedom because X is a real variable, but you can have simple systems like spin up or spin down which have just two degrees of freedom and then that is.

But for the description of this, we will use matrices.

Then, as is a chapter in the notes, quantum mechanics of the simple harmonic oscillator S central in quantum mechanics in a way as is in in classical mechanics, then angular momentum hydrogen Atom, the adaptation theory and variational method. Here. It really somewhat Maps on the chapters that we have, and in the end I still want to wrap up at the very end of the cause and try to make them contact with things that are even harder to understand than our.

Atomic physics and which are considered paradoxon.

So what comes beyond and that will be the last slide, so we will sort of stay in time with about 50 minutes when we have a session as such, because you may have a session at 11 and need maybe need of a convenience break, some coffee and even if you don't have to change from one lecture theater to the other, what comes beyond there is a an equation which is not really an equation but some truth in it. If you make quantum mechanics relativistic.

Then you have to do something that is called quantum field theory. QFT and quantum field theory is the conceptual framework upon which the whole standard model of particle physics is built.

And so if you have both courses, then you can study quantum field theory with us on the integrated master or MSE level. So there is a special module which is actually running in this semester, but you can't take it without having had quantum mechanics and relativity. So this is quantum field theory in itself, but then it's used in modern particle theory, is in another module and there is also another module from physics which teaches advanced quantum theory.

Which is also then really sort of applied quantum field theory for particle physics.

But you don't have to study it.

With respect to particle physics, even on the very bigger scale I talked about the smaller scale that without atoms that wouldn't be molecules. Without molecules we wouldn't be there. But even on the bigger scale nature cares about the quantum world.

So if you study at some point or read in Popular Science articles about the evolution of stars or the evolution of supernovae, what happens when they explode? How the energy is emitted? All these things depend on the quantum description of the world. So if we would make only tiny.

Tiny corrections to the framework that we're having here a lot of things would look vastly different.

So even the early universe soon after The Big Bang, if you would have things that there are in addition to the standard model of particle physics, things could look very different now.

So maybe there wouldn't be galaxies then. Maybe without galaxies we couldn't be there either.

So.

Let's say that's my very birdie introduction here, trying to put things in a framework and at the same time give you the technical introduction, the walkthrough, and what is required. So I want to just end with saying that despite all these really difficult circumstances, let's try to make the best of it and learn something new and exciting. And in the end also have some fun with it.

So I have talked a tiny bit too long. It always takes takes longer then then one.

And one one plans, but I will now stop my screen sharing.

And.

This is somewhat difficult here.

So and I will stop.