Operators in quantum mechanics

[@tannermiller5412]

These are the most easily understandable quantum mechanics videos I have ever found by a long shot. Keep up the great work!

[@jokerman9295]

Yeah these are some of the best explanations on the mathematics of quantum mechanics I have ever seen. Although Professor M is a little fast, I can always just rewind if I miss anything. I would have trouble keeping up in a live class of his though, good thing these are recordings.

[@oraange]

Hands down everyone ! This channel is far the best I 've ever met , from a french student

[@ProfessorMdoesScience]

:) Thanks for your support!

[@kaushikgupta1410]

Yes, Best for career building.

[@richardd7614]

These videos are so good. I think it was Richard Feynman who said if you think you understand quantum mechanics then you dont understand quantum mechanics, clearly Feynman never met Professor M does science.

[@ProfessorMdoesScience]

Thanks for the praise! :) But Feynman was a truly inspiring teacher and we cannot hope to compare ;)

[@sawanbhattacharyya3789]

I am an undergrad,thank you so much for these vedios it provides a cripsy idea and save me from getting frustrated by those hours long vedios and all I ended up with is with frustration and embarrassment.but your videos are so good and so crispy complex topic in elegant way. Love from India keep going

[@ProfessorMdoesScience]

Really glad you find them helpful, thanks for your kind comment! :)

[@workerpowernow]

another great video :) I hope your channel takes off because, I know from first hand experience, the usual hap hazard manner that QM is introduced can often be disorienting so having a rigorous and structured approach to the math underlying QM is invaluable. I have one small suggestion which is that you consider your presentation speed. I'm watching your videos to complement a linear algebra text that I'm working through in order to review material in greater depth before being thrown into higher level QM and I've found that, since I am trying to pay close attention and diligently take notes where helpful, I often pause your videos and have actually begun watching on 0.75 speed. This is of course not necessarily and issue, and one of the nice aspects of youtube (unlike an in person lecture) is that you can do just that. Additionally, I of course do not know if other viewers feel the same, but it's something I figured I would at least mention. Overall, wonderful video. Thank you

[@ProfessorMdoesScience]

Thanks for your support! And thanks for the suggestion, we're trying to slow down in the newer videos. However, I also agree with you that KZbin already provides the tools to cater to all needs: I too slow down/pause videos when I am learning something for the first time, but then go the other way and actually speed them up when I am simply revisiting something I already learned for a quick refresher. Overall, I agree with you that the video format provides a more useful flexibility than a normal lecture.

[@InSaNeXmANu]

Wow, you pedagogy is one of the best I've encountered so far, explanation+illustration are in very good coordination, makes it incredibly clear for such a complex topic ! Thanks !

[@ProfessorMdoesScience]

Thanks for your kind words! :)

[@cadespaulding3837]

this guy should be more popular

[@ProfessorMdoesScience]

Thanks for your support!

[@TheWingEmpire]

You are absolutely right

[@jatinsaini7790]

Quality of content at its peak!!!!

[@ProfessorMdoesScience]

Glad you like it! :)

[@s.31.l50]

Feel so lucky I came across this channel. I'm not studying anything related to quantum mechanics, but even I understood the video very well.

[@ProfessorMdoesScience]

This is great to hear, and welcome! :)

[@richardthomas3577]

Excellent! Thank you! These early videos serve as great reviews as well as good initial content.

[@ProfessorMdoesScience]

Glad you like them!

[@diyabatool1662]

excellent videos , helped me while I was reading the book

[@ProfessorMdoesScience]

Glad it helped!

[@MrOvipare]

Oh I wish I had these videos 10 years ago! There is great value in reviewing these concepts, I realize that I was confusing many things. I remember being super confused when we did the tensor product of states to create a new basis which could express entangled states. I think those were Bell states. My prof was calling this "le produit dyadique" which seems different to the outer product. Is it because in many-particle systems, each particle lives in its own distinct hillbert space? Reduced to working in a single hillbert space |u>

[@ProfessorMdoesScience]

The outer product we discuss here is different from the tensor product needed to describe entangled states. We do actually have a few videos covering tensor products, you can check them out here: kzbin.info/www/bejne/oauWY2NsiJd1bLM kzbin.info/www/bejne/imTcn6qOp6pjjtk I hope this helps!

[@MrOvipare]

@@ProfessorMdoesScience Thanks! :D

[@bryannac8541]

Great video! Thank you! I have a quantum midterm coming up and your videos provide the perfect review :)

[@ProfessorMdoesScience]

Glad you find them useful! Do spread the word ;)

[@karthikknarayanan776]

Thank you for taking the time to make these videos! I'm a first year uni student and this is great background knowledge for an MIT OCW course on quantum information science I'm taking.

[@ProfessorMdoesScience]

Glad you are finding it helpful! :)

[@password6975]

Absolutely brilliant

[@ProfessorMdoesScience]

Glad you like it!

[@wwmheat]

Thank you, Professor, this series is just awesome! I have a question: on 5:18 you are saying that the proposed expressions are equivalent by definition. Although intuitively it indeed seems right, could you please explain why it's rigorously true? And by definition of what? Thanks again!

[@elieh2194]

Just tremendously well done !!

[@ProfessorMdoesScience]

Glad you like it! :)

[@Mahedi71]

Thanks professor.🥰

[@ProfessorMdoesScience]

Glad it helps!

[@pabloweigandt4884]

In 10:45 you define the "inner product between a bra and a ket", but the inner product is between two kets, that is more or less equivalent to the action of a functional bra, acting on a ket (braket). The inner product is between the vectors of the same vector space.

[@ProfessorMdoesScience]

You are correct. I think in most videos we do say inner product between two kets, but we were clearly not careful enough here, thanks for pointing it out!

[@TheWingEmpire]

Awesome, can you describe how Hilbert space and Eigenvectors come together in quantum mechanics? I am a little confused

[@ProfessorMdoesScience]

The term Hilbert space technically refers to an infinite dimensional complex vector space with an inner product. In quantum mechanics, we are interested in both finite dimensional and infinite dimensional vector spaces. While you will often hear the term "Hilbert space" applied to both, in our vides we've decided to use the term "state space" to describe the most general case of both finite and inifinite dimensional spaces. You can find our video on state space here: kzbin.info/www/bejne/nnvSiIBvn8tjnbc Regarding eigenvectors (also called eigenstates or eigenkets), they are special vectors in state space associated with a particular operator, such that the action of that operator on them does not change their direction. We cover eigenstates in this video: kzbin.info/www/bejne/pmLdmGCZZtOprbM Overall, we go over the mathematical basis of quantum mechanics in our series on the "postulates of quantum mechanics", which you can follow in order in this playlist: kzbin.info/aero/PL8W2boV7eVfmMcKF-ljTvAJQ2z-vILSxb I hope this helps!

[@TheWingEmpire]

@@ProfessorMdoesScience really helpful!

[@LifeIzBeautiful10]

Nice presentation!

[@ProfessorMdoesScience]

Glad you like it!

[@-thesmartboard8984]

You're a life saver , thanks !

[@ProfessorMdoesScience]

Glad you like the video!

[@sayanjitb]

Dear sir, i was taught that operator can not act on bra vector , it always act on object what sits right to it. I am confused a bit now! Can you please help me out? TIA

[@ProfessorMdoesScience]

As a simple rule, operators act on kets, and their adjoints (i.e. the dual space equivalent of the operator) act on bras.

[@sayanjitb]

@@ProfessorMdoesScience thank you professor for the crisp answer! Love your channel from India

[@anubratasaha4367]

[@BruinChang]

No other words, only much thanks.

[@ProfessorMdoesScience]

Glad you like it! :)

[@judithkatongo3907]

i really like how you explain QM

[@ProfessorMdoesScience]

Glad you like it! :)

[@DrMarcoArmenta]

I've read in some papers the expression "The charge and flux variables are promoted to non-commuting observables". This means we put a hat to the charge and flux variables and they become operators. How does this work? I don't know how to convert a quantity to an operator. Do you just fix every eigenvalue to be the observations of, for example, charge, and then build the operator that has those eigenvalues?

[@ProfessorMdoesScience]

The quantization rule does indeed simply say that to go from classical to quantum mechanics, we need to promote the classical position and momentum to operators. With this, we can then also deal with derived quantities, like orbital angular momentum. There are some quantities in quantum mechanics, like the spin angular momentum, that do not have a classical analogue, and in that case we have to design the operator from scratch. Electric charge is not an operator in quantum mechanics, it is an intrinsic property of a particle. I hope this helps!

[@nastyavicodin6229]

Excellent videos, thank you a lot!

[@ProfessorMdoesScience]

Glad you like them!

[@vivekpanchal3338]

Hi, I have a doubt regarding operators, We usually expand the operators of the form, e^A, I have stumbled across [x e^p] commutation problem, Here normally we will expand e^p, but why it will be mistake full if we take x as, ln(base e) e^x in commutator relation and do further calculations ??

[@ProfessorMdoesScience]

The main challenge when working with functions of operators is that some of the usual rules we are used to when working with functions of scalars do not always work because operators don't always commute. For this reason it is typically most useful to work with the power series directly, as then all we have are products of operators, where all the commutation rules become clearer. We have a few videos going over some of these topics, so I encourage you to check them out: kzbin.info/aero/PL8W2boV7eVfnb10T_COKPozxEYzEKDwns In particular, the last video of the playlist covers functions of operators in some detail. I hope this helps!

[@vivekpanchal3338]

@@ProfessorMdoesScience Thanks, I got it 😊, Your videos are really very useful, 😊

[@pabloweigandt4884]

Very good.

[@ProfessorMdoesScience]

Glad you like it!

[@user-hm3su2et6s]

great video

[@ProfessorMdoesScience]

Thanks for watching! :)

[@gaurav510]

Thanks a lot

[@ProfessorMdoesScience]

Glad you like it!

[@pritamroy3766]

Hi professor M, my question is following, 1) we can write an operator in matrix form. Now lets say a matrix is acting on ket, and gives us a scalar times ket. Now my question is what will be the result if that matrix acts on bra instead ket??? Because operator or matrix can't differ wheather it is bra or ket . So what we'll get for this sandwich operation (< Bra | operator) | ket > = ??? And < Bra |( operator | ket >) = ???

[@ProfessorMdoesScience]

If I understand your question correctly, then both expressions should give the same final answer. I hope this helps!

[@pritamroy3766]

@@ProfessorMdoesScience thank you professor for your sincere effort And what about ,

[@ProfessorMdoesScience]

@@pritamroy3766 You can always calculate this expression, and perhaps a good way to understand what it would look like is to consider the matrix formulation: kzbin.info/www/bejne/rXran5VnocmMiqs And we do often deal with non-Hermitian operators in quantum mechanics, for example unitary operators play a very important role: kzbin.info/www/bejne/mJKshWl-lsaMq7M But at the end of the day, what you have to ask yourself is: of the many combinations of operators and states that one can build, which ones are the relevant ones for understanding the behavior of our system? And the postulates of quantum mechanics answer this question, for example telling us that physical observables are associated with Hermitian operators. I hope this helps!

[@sukumarsahoo7192]

very good explanation. But in Schrodinger Eqn does the hamiltonian operator changes the state after obtaining eigenvalues

[@ProfessorMdoesScience]

Operators act on states by, in general, changing them. If the states are eigenstates of the operator, then acting with the operator does not change those states, it simply multiplies them by the corresponding eigenvalue. If you are interested specifically on the Schrödinger equation, you can find more detail in our video: kzbin.info/www/bejne/eXzTqWyeoLZmfq8

[@sukumarsahoo7192]

Thank you

[@pabloweigandt4884]

In 13:00 you say that "one of the fundamental property of an operator is that is linear ...". An operator is linear or it is not.

[@ProfessorMdoesScience]

Should have clarified that we do work with linear operators.

[@moinakdey9268]

Hello Professor. The videos are excellent but would you mind if you could tell us about some books to refer to in case we want some practice . I need some suggestions of books to help me start with quantum mechanics. Thank you.

[@ProfessorMdoesScience]

We are hoping to prepare a video reviewing some of our favourite books, but good ones to get started with include: "Quantum Mechanics" by Cohen-Tannoudji, "Quantum Mechanics" by Merzbacher, "Modern Quantum Mechanics" by Sakurai, or "Principles of Quantum Mechanics" by Shankar. I hope this helps!

[@moinakdey9268]

@@ProfessorMdoesScience Thanks a lot sir.

[@ronaldjorgensen6839]

use inertia/momentum as void mass gravitation variable any variable isolated spedds operation of solve for AI chip unit

[@MajidMohammad2]

Well done

[@ProfessorMdoesScience]

Glad you like it! :)

[@zarasuleyman7]

Anybody who has done the exercise can tell about that? I actually don't know how to proceed in steps! :(

[@ProfessorMdoesScience]

What step are you referring to?

[@zamirbekmamatov2553]

I am new in quantum mechanics, so this seemed to be too confusing

[@ProfessorMdoesScience]

We are hoping to do a more introductory series in the future. But for now you are correct, these videos are roughly at the level of second/third year undergraduates who have already had an introductory course in quantum mechanics.

[@amaljeevk3950]

❤

[@snjy1619]

24/11/2023

[@tigab37]

These videos are saving me a LOT of embarrassment - bless you

[@ProfessorMdoesScience]

Glad to be helpful!