Transcript for:
Introduction to Quantum Mechanics I

okay so welcome to quantum mechanics one so for most of you this is the first time that you're going to get officially uh introduced to quantum mechanics and i'm very very excited to be the one uh doing that job quantum mechanics is perhaps my favorite subject within physics and i find it an amazingly interesting and exciting topic to discuss and i hope i can convey some of that excitement to you uh so this class you know you can interrupt me anytime you can ask me any question you know i am not the world expert on quantum mechanics so you know uh some of your questions i may not have the answer to if that is the case i will tell you and i will uh what i will try to do is that i will look it up or think about it and come back to you in the next class and so i wanted to be a very participatory class uh so um i will don't want to leave anyone behind that is my general philosophy so if you think that you are not able to cope with the class uh you know please ping me and i will try to help you outside class and if you have any questions uh academic or non-academic please feel free to reach out okay so um so now i before i you know get into the quantum mechanics stuff i want to talk about some grade distribution as well as some class policies okay so this is going to be probably the last of our offline semester and uh or not i don't really care one way or the other so um you know it'll be mostly caught on box so the great distribution is going to be something like this so there will be 10 participation quiz okay so what is participation quiz so uh what you will find is that when i post the lectures and the lectures will be essentially recorded in slightly edited version of the live classes once i post the lecture the lecture will be divided up into four to six or seven pieces and there will be interspersed with some quiz which will ensure that you have lost lecture the quizzes won't be very deep so this will be kind of low ball questions just to ensure that you have watch the lecture so if you attend the class there is actually unless you want to there is no reason to watch the lecture again you can just go ahead and do the quiz i don't care about whether you have watched the lecture or not as long as you have been able to do the quiz properly however i would encourage you if you missed the lecture to actually go and uh watch the lecture carefully because you know your exam and your assignment as well as tutorials will uh draw from what we're taught in the lecture okay so the participation quiz will be very easy if you just follow along you should be able to get 95 plus percent in the participation quiz okay okay and then what i just i actually have an attendance policy so you must attend at least 75 percent of the class if you do then you get 5 so attendance must be uh somebody wants to enter the class let me allow them okay so attendance must be equal to or greater than 75 percent so it's not like you know you get your you know proportion of five percent depending on how many classes you've attended no you get either you get the whole five percent or you get zero so suppose you get 74 of your attendance you may make a case with me and i might allow you but if you get if you suppose you know you attended seventy percent of the class then you will get zero percent of this five percent but if you attend seventy-five percent you get the total five percent so it's an easy five points and the rationale for having this attendance policy is so that you know you are encouraged to come to class you know sometimes because that your you might have intricate issues or you might have some stuff going on unexpected stuff you may not be able to you know join the class and i think you know 75 is a good enough uh you know attendance policy that it'll be you know it'll allow you to uh you know not be affected from such unforeseen circumstances if something does happen please reach out to me for example a few semesters ago one of my students he was based in a village which had very little very bad internet connection and he had to travel somewhere else to watch the lectures and i gave him waiver so he just watched the lectures on his own so if you think you're one of those cases please you know contact me okay so that's 15 percent of the grade taken care of so i'm going to introduce what i'm what is known as the tutorials and the tutorials are going to be ungraded but you are you must attempt the tutorial so you must have eighty percent tutorial attendance to pass if you have less than twenty eighty percent you will be failed in this course okay a lot of the learning that you will do in this course will be in tutorials so those of you who have taken my previous courses you know the format of the tutorial what i do is that i get somebody usually another a junior lecturer if i don't get that you know maybe an advanced student who will guide you through a pre written problem multi-part problem and it will solve that problem in a group helping each other okay so physics is a social enterprise it's a collaborative thing physics is highly competitive but the competition usually comes with between groups group a and group b when it comes to research but when group a is working they collaborate you know without reservation so i hope that in the tutorial you will learn how to collaborate and how to learn you will learn physics from each other through peer interaction okay so when you're in the tutorial don't be stingy help your friend okay now number four is that there would be there will be five four to five graded quizzes okay so five possibly and the graded quizzes will carry 15 okay so the graded quizzes are also very very uh they will be a little bit harder than the participation quiz quizzes but they will still be not very difficult if you pay attention okay and how many of graded quizzes there will be five graded quizzes and in this class you know there will there will be no best of policy okay there will be no best four or five or best three or four this sort of policy okay so there will be five that you know to help you i might do six credit quizzes but you know usually it turns out that uh we don't get time okay number five is this will be an assignment based course so you will get your thirty percent of the grades divided into four to five assignments okay now the assignment has very strict policy and the assignment policy is that you may collaborate you may collaborate in uh on the assignments okay but when writing up you must not copy each other and i cannot put enough emphasis on that you must not okay if i find um you know evidence of copying i will not call you in for questioning i will report you to the proctor's office and the proctor's office usually uh you will disqualify you will give you an f and you will lose your scholarship okay it is you know as much as i don't want that to happen i just don't have the bandwidth to deal with the people who are copying each from each other okay so this is you know i know that brac has a very strong culture of cheating unfortunately and i want to discourage that so this is my policy okay so are you is that clear with everyone yes sir yes you may you know you may ask each other oh uh can you help me understand this and you know when i was an undergraduate you know i used to uh you know discuss physics with lots of my friends you know we used to you know uh you know we used to discuss homework problems we used to discuss all kinds of issues uh subject matter but we never copied each other so you must you know write your own solutions okay it is very easy for me to you know to detect cheating i have a question about this yes when i help people sometimes i tell them kind of the algorithm that i use to compute something is that considered uh telling someone how you directly did something like i calculated this than that and that no i think i think that's fine i mean you know you should uh you should try to you know guide them towards that algorithm rather than telling them that because you know because we are actually not very as human beings we're not actually very good at uh algorithmic thinking yeah um i think we are uh you know because you know you know algorithm memorizing an algorithm without understanding it it's just very very difficult thing to do in my opinion uh so you know it's better to you actually it's easier to understand something right then the algorithm just comes out naturally you know and a lot of times you know a lot of times if the problem is interesting enough unfortunately undergraduate level it's not possible to have that many interesting problems but if the problem is interesting enough you can do it in more than one ways so you know at least superficially so you know algorithms um may or may not be helpful okay okay all right so any more questions on the assignments okay the other thing i'm going to do is that i actually provide help on the assignments i will actually be after posting the assignment after about a week or so i will actually have a special class where i will go through and discuss in the individual problems so there is really no excuse for you not to do the assignments and what i've seen is that a lot of you will not do the assignments on time even though they're you know the number of assignments is very doable it's uh four to five you know so i will encourage you i don't you know it's in your own interest to get the assignments in on time if you're late you know i i'm not very strict about that that i don't dock marks or anything but it's you know the the more you like postpone the assignment the the less you are engaged with the course okay so for your own sake you know i'm going to treat you like adults so for your own sake i highly encourage you to do the assignment on time okay and also because i will give you extra a very detailed help on the assignments okay um all right so then comes the midterm the midterm is going to be about 20 okay now the thing is that we are not sure how what format the midterm is going to be uh because you know we may or may not have offline midterm that is in person midterm uh but if it is online the way i like my midterm is that it's an open book it's an open book example and i discourage students from googling the um you know uh the problems because if you google the problem and you find you come across something very very like similar on the net and you just copy that it's actually very easy for me to kind of uh you know see that you are you are you know um indulging in what is known as plagiarism okay and that is not allowed according to the honor code so um so don't do that you know but you're welcome to use books you know that are assigned to the course you're welcome to use the lecture notes just don't you just don't talk to each other okay and what i do is that i the midterm will be you will be given four to five problems and you will have to do three problems and i will give you 24 hours to do those problems okay so the way i do it is that i take i one of the problems will be an easy problem that almost everyone can do the other four problems will be medium to hard problem so that students who are really paying attention students who are really engaged can make a difference okay and these are problems often these are problems i make up myself and so or you know i find them in some obscure book so it's in your interest you actually think about it yourself than trying to you know scour the internet to find the solution to these problems okay and and you will have one day right so time is not going to be an issue and i usually make sure that the exam is done on a day often it's on the weekend and i'm sorry for that but it's done on a day where it doesn't coincide with any other exam so that you can approach the problems in a relaxed manner right physics is about being relaxed and thinking in a relaxed fashion about at the natural world you should not be stressed about it so i try my best to make sure that that happens okay and number seven is 20 will be carried in the final or the equivalent assessment okay sometimes what i will do is that i will throw in a a graded quiz with the final or the midterm or it both and what will happen is that graded quiz will be contributing to this 50 15 okay so and yeah the final will have exactly the same policy as the midterm it's an open book exam okay and uh this is basically the grading policies do we have any questions no sir anyone else okay well if you if you have more questions later you can always uh you know you can always ping me all right so let's discuss some class policies okay this is very important okay so um as i've already already said you know there is a policy about collaboration highly encouraged copying highly discouraged okay and if you do copy if i find evidence of copying you will be reported to the proctor's office and the proctor's office has a reputation of dealing with these things in a heavy-handed manner unfortunately but there's nothing i can do about god okay the other thing is that if this is a no sexual harassment zone just one second okay i think my cat wants to come in my cat wanted to come in okay uh so this is no sexual harassment zone i feel like life should be a no sexual harassment zone and so i want to remind you that brac university is a safe place and i take this extremely seriously okay anyone who has found engaging in sexual harassment will be severely penalized and they will face expulsion from this course and depending on the severity of their you know of the you know act i may even disbar you from taking my future any of my future courses okay um so if on the other hand if you think that you are being sexually harassed please contact me as soon as possible if you don't feel safe contacting me contact the proctor's office um you know as much as possible strict confidentiality will be maintained okay so i've heard a lot of stories at brac where you know students will be working in groups and then some male student will then start messaging some female student you know sending them um messages even when the female student made it clear that that she is not interested in such advances you know the male student would you know persist that is not allowed that is not acceptable okay so this is i i take a very strong position on this okay so this is number one number two is that bullying okay we i also do not want to be there to be any bullying and and no no you know no bullying will be tolerated you guys are now adults so you're probably know that you know uh schoolyard bullying is not the kind of stuff that you know you do anymore but you'll be amazed that how many of my undergraduate students have told me that sir i have been bullied a lot of times it happens when the student is doing something which is perceived as not you know i don't know for example somebody asks you for a solution and you don't provide them with the solution so put pressure on you sometimes they will use the dominant culture to kind of you know give them the solution and they may resort to bullying for doing things like that so if you believe that you're being bullied please contact me as soon as possible the sooner you contact me the better the flip side of this is that i've seen many many students bullying their teachers at brec this is also unacceptable okay every semester especially in the large courses where there are 500 600 students there is a tendency for students to uh pressure the instructors to uh come you know to pass policies which will maximize their grades which will allow for longer time intervals so that they can go on various discord groups and you know stood and cheat and you know buy solutions we are aware of a lot of these things so uh you know in those cases i've seen that when teachers are strict when they say no we are going to have very strict you know windows for exams because you know you guys have not shown um that you can be trusted student sometimes resort to bullying for example a student was posting a poop emoji to everything that their teacher you know said so these are examples of harassment and bullying okay from the students to the teachers so if you have a problem with me and you feel not safe discussing it with me you can always you know email the academic complaints uh you know hotline or you can even approach the dean okay who is my superior and you know a lot of times you know um a friendly chat a mediation is uh you know will be will solve things okay so that is basically what i have to say in terms of class policies um i may have missed something uh do you guys have any questions or comments please you know you're welcome to speak out okay uh sir i was hoping that uh can the class can be shifted to a little earlier like in the morning or something uh mornings are very difficult for me i usually don't go to bed before three o'clock uh and don't get up before eleven sometimes even one o'clock uh but you know we can what's your issue what uh what's the problem you have uh usually sir at this time i teach my students so it's actually a class so maybe two or two one or two would be good but if it's not possible then i will differ my food so yeah are you money is this a private coaching thing or something like that yes sir i teach i i have much okay um yeah maybe you know we you should uh try to do that because you know we don't want to inconvenience everyone because i wanted to i want to actually usually i change the class time every semester uh but this semester i i'm actually mindful of trying not to change the class time because otherwise students will all some students will be inconvenienced right because they will it'll clash with some others so i wanted to keep this slot so see if you can do it if you can't do it then you're always welcome to watch the lectures later and i will give you uh a waiver about attending the class okay okay thank you but but about the waiver i must warn you that you know usually it takes me a day or two before i get around to posting the lecture lecture okay so you'll be a little bit you know in a time there'll be a phase difference between it usually doesn't affect very big in a major area but you know um so see if we can have a proper one okay okay okay anyone else no sir all right um okay my cat is trying to get on the computer um he wants to be badly part of the class uh okay so um so i also want to discuss the timing for the tutorial okay sorry about that um let me go back to this um okay so i want to discuss the timing of the tutorials so usually what i do is that i have the tutorial class on saturday um so i'm going to propose that maybe saturday 3 30 could be a good time uh if that doesn't work you know maybe the other option would be a thursday 3 30 slot but i understand that some of you might have classes on thursday 3 30. can we uh have like can people tell me this sounds good okay saturday 3 30 yeah i go for saturday okay saturday is good with me okay okay saturday 3 30 okay so i still haven't recruited the person who will be teaching the tutorial class uh but i will do it this week and hopefully by next week we can start the tutorial so you know some usually the tutorial class is about one and a half hours uh but i actually encourage you to work longer until you have solved the problem so i will try to recruit someone who is who will not be very stingy with their time okay um the another thing about the tutorial is that you don't always have to finish 100 of the tutorial about 80 percent of the tutorial if you finish it should be actually good the rest you can do it on your own and then uh you will be asked on a the roster of people you will be asked to write the solution collaboratively in a nice you know way and then post it um you know and your your your after i've checked the solution it'll be posted officially on slack and uploaded onto the ux page okay so so is it decided that uh it'll be saturday 3 30. okay so what i will do today after class is that i will make a google calendar uh like uh for this course uh the google calendar you know schedule and i will share it with you and i think if you accept invitation through your g-suite account then uh in future classes you don't have to ask for permission to commit you can just come in you know uh automatically okay so the tutorial again let me just remind you i your half your attendance is required at least 85 80 percent of the time okay so attendance because i think that the physics is really learned in uh solving problems and the tutorial is basically a regular way of ensuring that you solve problems okay okay any questions okay the last thing i want to discuss is something slightly different it's a it's about mental health okay so you know the pandemic has put a lot of pressure on us in terms of our family life in terms of our mental health right um you know this uh you know many of the students i know their parents have lost jobs uh loss you know of income that has put pressures on the you know how uh how much there they can support their kids so and you know as well as you know for example you know um many of you actually support yourself by doing uh by teaching for example jabbar just said that you know he has to uh teach students right so many of my students are doing that so so i want to so all i'm trying to say is that you know the it's not very easy to be able it's not always easy to be able to navigate the pressures of the modern world and you know what i would want ideally is that i would want this course to be something that does not cause your mental health issues but you know uh causes you joy okay but of course that's not always going to be uh you know the case because whenever you challenge yourself in life you know stress is a integral part of it now the whole point of stress is that you want to be able to manage the stress okay so there is stress which is manageable and stress which is not manageable and stress becomes too unmanageable that's really what leads to you know breakdown in mental health and just like physical bodies you know each of us have different mental makeup so you know someone might might find taking a you know you know might find it very easy to take a lot of you know um commitments and pressures and but you know someone else might find it very hard to take on the same amount of uh meant you know commitments the point is that you know um you should never compare yourself with others we are all unique uh you know if you know um there's some kind of buddhist saying that you know you cannot really be somebody else because that place is already taken right so you should always celebrate the person that you are he should uh you know um so if you're having and i'm extremely like uh sympathetic and understanding of mental health challenges that students go through and you know and what kind of you know and i try to accommodate those things okay and as long as it's genuine so if you're if you're facing challenges suppose you're having problem concentrating you know don't feel ashamed don't feel judged please contact me the sooner you contact me the more help i can provide you the more support i can provide you unfortunately our in bangladeshi culture as well as you know bangladeshi society you know uh mental health is a taboo subject and i just want to change that i want to change that and i want to change that by admitting that i myself have suffered severe mental health challenges in my life i've had nervous breakdowns i suffer from anxiety i take an antidepressant if the anxiety gets extremely bad i have emergency medication for that i do regular meditation i've been doing meditation for five or six years and that has helped me immensely and you know and you know i have overcome to a large extent the stigma that is attached to mental health challenges okay and i found that by overcoming by you know by not attaching shame or letting go of that shame and stuff like that you know i am much more uh relaxed and i'm much more happy and i'm much more engaged okay so this is something i want to encourage you there are lots of free resources for meditation these days you know a lot of resources for uh youtube you know free apps uh you know lots of stuff like that so if you are interested you can always reach out to me in a private message and i will try to you know help you in any way and if you are facing pressure family pressure you know financial pressure and stuff like that please reach out to me and i will do my best to provide you with support okay any comment or questions uh i'd just like to add that alongside meditation if it's possible it's better to just go out for a walk like i know it's uh it's dynamic but going out for walks has helped me actually tremendously and i feel much better through meditation and exercise and going out yeah yeah well actually you know going out for walks in open space you know that's not that is that is actually good for your health you know because you're not you know there's enough air that the virus will get uh diluted just don't go out for walks in joguna future park right now without a mask you know go out where there's fresh air right uh it's hard to find in dhaka but you know but i think i agree with josh 100 um or or a bicycle ride whatever works for you right you know okay anyone else wants to chip in thank you very much for josh for that suggestion or you can play video games right some people play video games you know uh some people do uh yoga you know so all right so okay so you know this is i don't want to close this topic because this is an ongoing discussion and please you know if you are have any issues reach out to me okay okay any more questions in general about anything no sir okay in that case let us move on and discuss something about quantum mechanics and let us just let me just like give you the outline of the kind of stuff that i want to cover in terms of course content in this course okay so um although this is becoming less and less popular i actually think that it's always a good idea to ask the question you know why like do we need quantum mechanics okay quantum mechanics is extremely weird it's uh i would say it's uh it's weird it's beautiful in a weird way okay and uh but you know no one very few people could have come up with the structure of quantum mechanics so we will start with some semi-historical comments about quantum mechanics okay so some history it won't be we are not interested in teaching historical quantum mechanics but you know a little bit of his history is going to be in my opinion helpful so but the topic of this course is non-relativistic quantum mechanics so you know the main topic is non-relativistic quantum mechanics the interest you know you might say why not relativistic quantum mechanics and that would be a very good question the relativistic quantum mechanics should follow from this but actually there's a deeper reason it turns out that when you try to marry quantum mechanics with relativity quantum mechanics doesn't say stay the same it actually naturally leads to a new subject which is called quantum field theory and that is why usually uh in courses uh in in universities you see courses on ron writers say quantum mechanics and then quantum field theory so the basic equation for non-relativistic quantum mechanics is the schrodinger equation the schrodinger equation so we shall discuss the schrodinger equation in detail okay so there is a parallel formulation of quantum mechanics which is not in terms of schrodinger equation but in terms of an operator algebra in its equation and those equations are known as the heisenberg equations okay now the heisenberg equations and the shorting for some time after the you know uh these two different uh formulations of quantum mechanics uh you know were discovered uh they it it was of course observed that they both predicted the same experimental values so it which is like weird because they seem to be completely different so what happened was that it was then dirac paul adrian maurice dirac who was able to show that the schrodinger equation and the heisenberg equations are actually equivalent by doing that what dirac did is that he elucidated the underlying linear algebraic structure of quantum mechanics so giraffe did very very important work in that uh line and i cannot but you know uh note here that dirac also came up with the first came up you know with the first successful relativistic quantum mechanical equation this equation was the equation for the electron but the equation also predicted that there be an ant electron so dirac actually in trying to marry quantum mechanics relativity he actually um predicted the existence of anti-particles and why did i say successful here because before dirac there were many unsuccessful attempts in marrying quantum mechanics with relativity and in fact schrodinger himself found an equation which is now known as the klein gordon equation we and the klein gordon equation is consistent with relativity but unfortunately it's not consistent with the uh with the probabilistic interpretation of quantum mechanics and that's why it was abandoned and then until dirac discovered a different equation the klein gordon equation has a quantum field theory interpretation but that's something that is beyond the scope of this lecture okay so we will be taking the route of mainly discussing quantum mechanics from the point of view of the schrodinger equation but i will tell you how the schrodinger equation is related to the heisenberg equation okay so we won't entirely ignore the heisenberg equations the heisenberg equations become very useful at when you you study say quantum field theory for example so there's another interpretation there many another way of looking at quantum mechanics and that's known as the path integral interpretation and this is by due to feinman although he was inspired by dirac okay he was inspired by a cryptic comment in direct book and he wanted to understand that comment and he ended up discovering a new way of formulating quantum mechanics unfortunately our course will not cover the pathological interpretation it will be covered in a either in quantum mechanics 2 or quantum mechanics 3 okay but if any of you are interested in path integral i highly encourage you to read the book by 5 million hips okay fine man uh sorry it's only one n and hibs they wrote a really nice book on the pathological formulation of quantum mechanics so here you know it's a it's a textbook it's an introductory textbook you can always read that all right so um after that uh what we'll do is that by the way any questions please do interrupt okay prepare any questions so schrodinger equation the formulation of quantum mechanics in terms of schrodinger equation is known as wave mechanics because as we shall see the schrodinger equation is the is the kind of wave equation okay it's a wave equation so you might say how does a wave equation describe quantum mechanical particles and that's a very good question the way it works is that to each quantum particle in fact each quantum system you can associate a wave function say it's i usually generate psi but we'll use other symbols such as phi etc this is a wave function and it's a mathematical object which is a complex function it's a complex function of uh time okay and the schrodinger equation describes how this wave function evolves in time and what you will see is that according to the postulates of quantum mechanics the wave function if you take the wave function and you square it so if you say do something like this take the wave function and you square it and this gives you the probability density the probability density of finding the particle particle in some state and that state could be say in a certain region of space or that state could be uh the you know the energy of the particle or the momentum of the particle you know we will detail discuss those things in detail later okay so today i'm just kind of warming up the whole thing today it's going to be uh somewhat non-technical okay okay so uh do you have any questions by the way you guys have been suspiciously silent uh no question sir exactly so far all right okay all right so uh that is our next thing um so then what we will do is that we will basically um apply this to some simple one-dimensional system okay so simple one-dimensional systems so these are systems that we will solve very explicitly but i will do a more general like analysis of the schrodinger equation in 3d and for this we will need a lot of linear algebra we will need in fact we will need fourier analysis and you will see that fourier analysis is essentially an infinite dimensional version of linear algebra okay so when we're doing this we will also introduce some you know the postulates of quantum mechanics so for example some mathematical ideas such as a hilbert space um hermitian operators stuff like that okay unfortunately quantum mechanics is quite mathematical well that's the way nature is you know we physicists don't like learning mathematics unless they need it for some application it turns out that quantum mechanics is quite mathematical so you have to learn some mathematics okay so for example dirac as i said before direct elucidated the uh linear algebraic structure of quantum mechanics but dirac was not big on proofs okay he was not an analyst so the mathematical foundation of quantum mechanics was put on firm footing by someone else do you know the name of that person his name was johnny von neumann uh johnny von neumann was probably one of the greatest mathematicians of the 20th century he also laid the foundation of the modern computer along with alan turing he was a faculty at princeton and he wrote a very famous and influential uh book on on quantum mechanics called uh the principle the mathematical principles of quantum mechanics i think that's what it's called yeah in which he talked about convergences the existence of you know states as my father you know what does the wave function actually mean you know uh issues that has to do with convergence and stuff like that okay so we won't go into these mathematical foundation but i want you to be aware that there are a lot of mathematical niceties and subtleties in quantum mechanics which were a lot of which was resolved by johnny for neumann okay okay so so we are going to do one dimensional quantum mechanics and then we are going to discuss a very very important problem like a system which is called the one-dimensional simple harmonic oscillator okay the simple harmonic oscillator is kind of the foundation of most of quantum mechanical examples that we see out there and the simple harmonic oscillator it is so important that we will solve it in two different ways so we will solve it in two different ways one would be by solving schrodinger's equation another way is going to be a very beautiful and elegant method introduced by dirac which uses the algebra of the operators okay [Music] and then i want to shift gears and i want to talk about you know identical particles and quantum statistics okay now quantum particles are identical like two electrons are the same so they're not like twins so for example if we have two twins they may look identical but they are uh different people you know if you know but if you have two electrons and if you put them in a bag then when we take those electrons out again there is no way of telling which electron is which okay so suppose that there is some box black box and there's an electron a say coming in and an electron b coming in and afterwards suppose that you know the electrons go out there is no meaningful way in which you can say that this is say electron a and this is electron b you know this doesn't work and this has the fact that electron a and electron b are identical has consequence in terms of their statistics meaning that you can actually predict the you know there are predictions based on the fact that they are not identical and it's not just electrons which are safe spin half particles as you will as you will see it's also a diff so they're different kinds of particles okay and depending on their spins they will have different statistics so i want to cover that as well so they're fermions and they're bosons they're two kind of statistics in three dimensions in three dimensions three spatial dimensions there are fermions and there are bosons okay i should uh use um a small f because fermions are named after a fermi and they follow what is known as the fermi dirac statistics and bozos were discovered by bose and then einstein did very important work on that he found a he found einstein based on the work that bose had done einstein found a new state of matter which is now known as a bose-einstein condensate and this was you know discovered experimentally um i think in the 80s or something and you know there's a nobel prize given on it and if you were in my stepmet class we actually covered the basics of bozeinstein condensation but of course we won't do that here but i want to introduce you to the idea of quantum statistics okay all right so after that the next topic is an optional topic it i will probably not be able to cover it because of time constraint but i just want to mention it is that you know the analysis of the angular or the angular momentum algebra okay so angular momentum in and 3d systems okay so you know the type of particles that we have like fermions and bosons they can take very very specific angular momentum values these are known as pin values but it's also very specific to three dimensions okay if you were in two dimensions particles actually can have a more general statistics and that statistics is known as anionic statistics and you might say okay we don't live in a two-dimensional world so why do i care you actually can find systems which are very thin so that they're effectively two-dimensional quantum systems and in such systems there are what are known as pseudo particles okay pseudo particles and these are kind of vortices and and they act like particles so you can have associate you know wave functions with them if you look at very high energy like if you look inside you will see that there are some complicated bound state of say electrons and phonons but you know but above a certain length scale they look like particles and these are called pseudo particles and you can have an effective quantum mechanical description of those things and it turns out that they can have more general statistics and that's known as anionic statistics and there's a lot of very beautiful physics and mathematics related to anionic statistics which has to do with say not theory braiding or braided algebra uh you know stuff like that okay and right now there's a lot of experimental um you know work that is being done so it's a very rich field okay so but i'm not sure that if i can cover the three-dimensional angular momentum uh because i probably won't have time and that's because the last one-fourth or the one-third of the course what i want to do is that i want to introduce you to the basics of quantum information okay there's no reason for me not to introduce it in an introductory class in fact there is a textbook written by ben schumacher and michael westmoreland which introduces quantum mechanics from the quantum information point of view okay so this will involve you know what is a qubit that is a quantum bit uh then you know although the idea of a density matrix is applicable to many things but the idea of a density matrix is especially useful in quantum information and then we will discuss you know the basics of quantum circuits okay circuits and maybe some simple algorithms quantum algorithms as well as say um yeah quantum algorithms we won't really be discussing physical realizations that's a bit beyond this course but this is what we want to end the course with okay so any questions this is kind of in the realm of quantum computing right yes that's why i'm calling this condom information yeah so this is you know going to be a hot topic in the future uh hopefully so i want you guys to be you know i want you to know the basics of it okay how what are the basic fundamental ideas you know and i think uh um csc used to have a quantum information class i'm not sure what the status of that is anymore because uh the person who taught it was if left for his phd but you know we can revive that does anyone know if fcs is still offering that course um cc is offering quantum computing this semester okay so that's the thing here so uh there will be some overlap between quantum computing and chrono and and what i'm what i'm saying and oh yeah i also want to say talk about teleportation quantum teleportation and um yeah this will be very basic but this is this is the aim okay any more questions or comments so let's consider today's class lecture zero and i won't get into the stuff uh the you know i won't get into the nitty-gritty today but in the next class we will start by discussing the limits of classical physics and why we need quantum mechanics okay okay do you have any questions in general i do have a little bit of a silly question but is there a difference between quantum mechanics and quantum physics because i hear people saying both of those terms no no there isn't it's uh it's it's usually used um interchangeably so essentially you know what we call quantum mechanics came from schrodinger called it wave mechanics mechanics because it deals with particles waves because the fundamental equation is a wave wave equation so this was what schwinger called this and uh but how it worked realized that he formulated quantum mechanics in terms of the observables like energy momentum stuff like that and he what he realized was that those observables did not commute and his friend pasqual jordan told him that oh yeah those are described by something called matrices so what heisenberg called his version of quantum mechanics was called matrix mechanics okay and the word quantum was introduced in 1901 by max plunk okay when he realized that when he tried when he came up with the formula that describes the radiation of a black body that is at a certain temperature accurately he had to postulate that atoms which make up the hot black body you know their energy state was given by an integer times a small constant times uh a frequency and that constant h is called planck's constant planck's constant but so the energy of the oscillators that make up the atoms he approximated the atoms by oscillators and you know the energy is then what it's quantized right because it comes in uh discrete values so quantum means discrete and quanta is a disk so and because of that you know planck called this the you know uh this quantum planck's constant is also called the i think the quantum of action fancy name um this has by the way planck's constant h its dimension is that of angular momentum okay and you might say y angular momentum and that's because it has the same dimension as a volume element of a like a two-dimensional phase space okay and the phase space has a two-dimensional phase space has the um volume element the dimension of that is actually uh it has the dimension of angular momentum okay so because of that i think wave mechanics and matrix mechanics got merged into quantum mechanics but more recently you know people have been kind of looking at quantum mechanics and thinking of you know like mechanics is kind of an old-fashioned term so a lot of people use quantum physics in instead okay so quantum physics is usually um thought of as a catch-all term for both quantum mechanics as well as chrono field theory okay as well as a quantum gravity so sometimes it's used equivalently to quantum mechanics sometimes it means all these things so you know this is just a very um informal way of of talking about quantum mechanics in fact at psi where i taught for 10 years uh our uh introductory course on quantum mechanics was called quantum physics it was not called quantum mechanics in fact that course had a very quantum information flavor uh because you know psi had pi is one of the world's leading centers uh well waterloo is a world leading center for quantum information uh the quant the um iqc institute for quantum computing is there and that actually grew out that was an outgrowth of the perimeter institute okay there is also quantum electrodynamics and quantum thermodynamics are there yes so these are yeah that's a very good question and those are part of quantum physics yes they're a little bit different from quantum mechanics but their applications of quantum mechanics to uh so the first one quantum electrodynamics is an application of quantum field theory to electro electrodynamics which was um you know pioneered by feynman uh tomonaga schwinger and freeman dyson although freeman dyson was not given the nobel prize for that uh but freeman dyson had an equally important role to play uh there so um so that's so so quantum electrodynamics known as qed is essentially the quantum field theory of electrodynamics okay how uh like um you know electrons interact with photons right that's electrodynamics and so quantum thermodynamics is essentially the application of quantum mechanics to thermal physics okay thermal physics and thermodynamics okay dynamics and there's also quantum statistical mechanics right which is very similar so the quantum statistical mechanics because you know as you know from statistical mechanics the probability that a particle has energy e is given by the boltzmann factor in the uh in the micro in the canonical ensemble right and uh sorry the canonical ensemble or the macroeconomic yeah in the canonical ensemble so um and this is becomes slightly changed depending on the statistics of the particle you know if you have a boson or a fermion so you know there are some um subtleties to the statement and uh so those are covered in in quantum statistical mechanics i think in my statistical mechanics course i did do quite a bit of quantum statistical mechanics i i think uh it was that mashiku who said that this this comment um sorry sir who was it who uh talked about condom stuff was it i think it was not me okay i don't think you were in my statement course right no sir um i the only physics course that i did so far was uh physics 202 which was last semester so this is my second physics course into the minor okay so you know another thing that i people ask me is that what are the you know prerequisite for this course uh there isn't a lot but having some mc but you must have mechanics at least and having some electromagnetism is helpful but it's not essential so it you know it'll be a sophisticated course but it doesn't have a lot of um prerequisite some having some linear algebra is also very useful but i find that the way that linear algebra is taught as an undergraduate level at brack is not very helpful for quantum mechanics because the way linear algebra is taught in mathematics in this country it's its emphasis is more on just uh you know learning some algorithms by heart you know or by or memorizing algorithm rather than understanding the underlying mathematical ideas of vector spaces in this course we are going to be more emphasizing on the underlying ideas of a vector space and how that relates to quantum mechanics so in some sense i will be teaching you linear algebra from scratch hopefully okay any questions or comments um sir is there any specific book that we're gonna follow or like oh yeah yeah there will be a several books i will i will post those names um i didn't get the chance to post those names when i made the ux page i i will update that page uh maybe tonight so one of the books i really like is uh is skinner and bini it's a recent book an excellent book i also like very much shankar uh i also like an old book which i learned quantum mechanics from poland i think crazeman or something like this and um these are uh there's an advanced book by uh sakurai and somebody else sakurai died before he could publish it uh this is something i will use from time to time not really very um and uh oh there's also a book by taylor and french an old book and i find that the treatment of one dimensional system is excellent in taylor and french so i will be using these books a lot okay and for um quantum information i haven't decided yet i might be using a lot of the uh west moorland and schumacher book okay and so this is for quantum information there is another famous book by quantum information but uh on conor information is by nielsen and chuang uh it's a bit mathematical but it's also a good book i i learned quran information from this book so yeah i will post more detail of this there are a few more books which i also look at from time to time i will also post those names okay so yeah i'm not keeping anything secret from you okay you will have this you will have access to all the resources that i use obviously one thing is that never use like uh indian notebooks okay when we were kids when we were undergraduates a lot of us teachers would recommend so the india has this sort of you know culture of using notebooks and they were the worst books to learn from you the basic people who studied those books essentially learned didn't learn any any physics shankar is indian but of course shankar is not writing an indian notebook he's a he's a faculty at yale i'm not saying that indian faculties are bad but there is a culture in bangladesh of using uh notebooks which were used in indian like you know past course and those kind of um you know exams so never you know always use good books those are basically like information dumps right i think i've seen them before yeah exactly the information dumpsters but they're not they actually have they actually have wrong information all the times so will you be uploading sorry yeah i'll be uploading my lecture notes yes no i was gonna ask that if uh will you be like uploading the like the title with the authors or will you be uploading downloadable links of the books uh i will i will upload the title with the authors because the downloadable links i think you guys are smart enough to find for yourself and i i'll i'll be violating some copyright you know um policy if i do that okay i actually like personally and i appreciate i mean when you go to say jen and you know you you all these books will be available in libya okay but i actually own most of these books myself because i love having physical books but that's just me i'm from an older generation so okay yeah i should have every one of these books okay any more questions or comments sir i have another question yeah sorry it was regarding the tutorials like basically it's going to be like so is it going to be like a hands-on uh problem-solving session like where you do it in groups with with like a supervisor or something like that yes and so what i'll do is that you know there'll be a discord uh like a server or something and the person who is going to be running the tutorial they will make uh like a different uh uh different like rooms or i don't know what to call them i actually haven't i've never actually like used discord myself and but it's easy to make different rooms in discord it's not possible to do that in google meet as far as i know and you will be working in small groups of three or four four four or five and what will happen is that the supervisor or the on the ta or the st they will go from one room to another and they will just observe and maybe help you uh you know get along by asking you questions so they're not going to provide you with the solution they're going to help you reach find the solution okay so we'll be having a a ta throughout this course right uh i hope so i haven't chosen the ta yet because it's going to be a tough press tough choice and it'll be it's it's not going to be an easy course so i have to choose a ta very very carefully