Angular momentum eigenvalues

[@henryhop462]

I cant believe how clear this explanation was. I have worked through the entire section of the angular momentum topic up until this video so far. Im completely mindblown. I have struggled through so many theoretical physics lecturers with arrogant Professors and, from an teaching point of view, incompetent phd students in my bachelors degree.... Im close to tears right now. This reignites my believe in Physics education. Keep up the great work Professor M does Science team! :.)

[@ProfessorMdoesScience]

Glad to hear you are enjoying our videos! Comments like yours really motivate us to keep going. Where are you studying?

[@tianruiche3639]

@@ProfessorMdoesScience think he can't tell you that after he spoke ill of his professor🤫

[@stranger3944]

The books had me confused with all those legendre equations..thanks for saving me...very lucid explanation.. truly marvellous work

[@ProfessorMdoesScience]

Glad our approach proved helpful! :)

[@joaovictormacedosales2520]

This channel is incredible! You are doing some great work by building the theory from scratch. With these lectures and Cohen-Tannoudji's book under the belt, I feel tremendously motivated to study. Lots of gratitude from Brazil!

[@ProfessorMdoesScience]

Thanks for your kind words, and glad you like it! :)

[@dutonic]

21:22 Writing this because it took me a while to figure out why μ,max = (n/2)ħ. The leap in logic was not obvious to me at all. The reason why this is, is because n is a sum of both p and q, which are representative of single intervals of ħ. Without diving n by 2, n would be representative of intervals across this number line of 2ħ instead of ħ, which is what we want.

[@ProfessorMdoesScience]

Glad you sorted it out, we should have been clearer!

[@guoxinxin693]

This is a truely beautiful show of quantum mechanics!

[@ProfessorMdoesScience]

Thanks for your continued support, and glad you are enjoying the videos! :)

[@richardthomas3577]

I think this is your best angular momentum video, and that is truly saying something. I am working through old QM textbooks by Gasiorowiscz and Merxbacher, and honestly (although I love those texts) your videos are basically a beacon of clarity. I find I can work problems much much better after watching your videos, because you extract the key concepts in a clear, concise fashion (which cannot always be said of the texts). Again, Thank You for all the hard work you obviously put into these videos.

[@ProfessorMdoesScience]

Wow! Thanks for your kind words! :)

[@thiruniwennawattage9424]

U

[@jayminshah5565]

You guys are probably going to save my life....Thanks

[@ProfessorMdoesScience]

Glad to hear our videos are useful!

[@jacobvandijk6525]

@ 23:15 MORE SPECIFICALLY: n = even for orbital angular momentum and n = odd for internal angular momentum (spin) ( kzbin.info/www/bejne/a5mYnpWCateWpZI )

[@kunalshukla1236]

That sound in the beginning when science comes down frightens me everytime.

[@ProfessorMdoesScience]

Oh dear :)

[@amirrezaadham7308]

this is reallllly the best video that I have watched until now about quantum. thank you so much. :)

[@ProfessorMdoesScience]

Glad you like it! :)

[@armalify]

This channel must have more subscribers !

[@ProfessorMdoesScience]

Thanks for your support! :)

[@shashankarunkumar7867]

I wonder why Griffiths made things more complicated by covering Hydrogen atom before angular momentum. I really liked your approach, and it has made spherical harmonics much clearer to me. Thanks for the amazing videos, I appreciate all the work put into this!

[@ProfessorMdoesScience]

Glad you like our approach! Indeed, doing angular momentum before hydrogen should greatly help understanding :)

[@gabriellarata0543]

Hi, I've just found your videos last night and they are brilliant! It has been very helpful for me because I'm having only online classes right now and sometimes I just get lost in the middle of the class. Your videos about the angular momentum are helping me get through this. Thank you very much for your work!! Sorry for my bad english!

[@ProfessorMdoesScience]

Really glad to hear you find our videos useful! :)

[@shayanmoosavi9139]

Wow, now I completely understand why angular momentum is quantized. Griffith made it look like it completely came out of the blue and his arguments usually won't satisfy me, I'll have to go to shankar for a more rigorous explanation. Thank you so much for the very clear explanation, you've gained a new subscriber :) Do you have any recommendations for an undergraduate QM textbook other than shankar that also has a clear explanation?

[@ProfessorMdoesScience]

Glad you liked it and thanks for your support! Another textbook I like is Cohen-Tannoudji, which starts from scratch and does not skip any of the details.

[@shayanmoosavi9139]

@@ProfessorMdoesScience thanks, I'll check it out.

[@universum-theuniverseexpla6565]

these are high quality physics videos, great job!

[@ProfessorMdoesScience]

Glad you like them! :)

[@noelwass4738]

Excellent exposition and thoroughly enjoyable!

[@ProfessorMdoesScience]

Thanks for watching!

[@LifeIzBeautiful10]

Great explanation and illustrations!

[@ProfessorMdoesScience]

Glad you liked it!

[@bhoopendragupta4782]

Thanks for this beautiful explanation. You made this so easy. 👍

[@ProfessorMdoesScience]

Glad you liked this! :)

[@crimemastergogo4156]

You are doing great job.Please also upload lectures on perturbation theory

[@ProfessorMdoesScience]

We plan to do videos on approximation methods (including perturbation theory), but it will still take some months before we get there!

[@MrZzzjjj]

Wow I wish I discovered this channel sooner.

[@ProfessorMdoesScience]

Welcome, and we hope to see more of you in the future! :)

[@sayanjitb]

At the playback time 19:46 mu_Max^2 + mu_max h = mu_min^2 -mu_min h => mu_max = - mu_min, how? does it mean mu_max^2 = mu_min^2? And also since \mu^2

[@ProfessorMdoesScience]

Yes, if mu_max = -mu_min, then mu_max^2=mu_min^2 because (-1)^2=1. Therefore, mu_max = -mu_min is the solution to the first equation you write. For your second question, if you take mu=sqrt(lambda), then you can apply the raising operator L+ and would obtain a state with mu=sqrt(lambda)+hbar, which is forbidden. This means that mu cannot be equal to sqrt(lambda). You could also prove it going the other way, applying L- enough times to get an eigenvalue smaller than -sqrt(lambda). The only values that terminate the ladder are mu_min and mu_max.

[@sayanjitb]

@@ProfessorMdoesScience Thank you so much indeed. I found this channel very helpful than anything else.

[@quantum4everyone]

The equation, for a fixed mu_min is a quadratic equation for mu_max. Solving it, you find mu_max=-mu_min or mu_max=mu_min+1. The second solution cannot occur, because mu_min

[@andreapaolino5905]

Awesome content! Is there any chance you will ever upload some videos on the addition of angular momentum?

[@ProfessorMdoesScience]

We hope to publish a series on spin angular momentum soon, and after that we would do addition of angular momentum :)

[@andreapaolino5905]

@@ProfessorMdoesScience wooooooow

[@raptorhacker599]

hello. does this answer the question : Obtain the eigen functions and eigen value spectrum of general angular momentum operator J?

[@ProfessorMdoesScience]

The video does answer the question as to what are the eigenvalues of a general angular momentum operator J. For the eigenstates, you may want more information to fully characterize them. We have covered in some detail the eigenstates of orbital angular momentum (corresponding to integer j values) in this video: kzbin.info/www/bejne/fZyViYGjfq2JrdE We are planning a series on spin, which will give more detail about half-integer j values. I hope this helps!

[@anubratasaha4367]

Can it happen for a physical system that there are two or more values of "j"? Like \hbar (j = 0) and (3/4)(\hbar)^2 (j = 1) are the (repeated) eigenvalues of J^2?

[@ProfessorMdoesScience]

If I understand your question correctly, then the answer is yes: different j values label the different eigenstates of J^2, but we can have a system which is in a superposition state of various eigenstates. I hope this helps!

[@anubratasaha4367]

@@ProfessorMdoesScience Thank you!

[@tomasbrage4450]

Hi, I just would like to let you know that we will be using your videos in our Atomic and Molecular course, especially for basic QM, to introduce the AM and looking at two-body systems. Since it will be a part of the teaching material, I would just like to let you know - a fair thing between teachers. Tomas Brage, Professor of Physics, Lund University, Sweden

[@ProfessorMdoesScience]

This is great, and thanks for letting us know! We would be keen to hear more about how you are integrating our videos in your course, and also if you or the students have any feedback.

[@mdsspace-time2557]

Please make videos on Spin, thanks for your awesome classes

[@ProfessorMdoesScience]

We will definitely cover spin in future videos!

[@amaljeevk3950]

How beautifuly explained ❤

[@ProfessorMdoesScience]

Glad you like it!

[@ernek89]

This is great! Thank you

[@ProfessorMdoesScience]

Glad you like it!

[@workerpowernow]

very clear explanations

[@ProfessorMdoesScience]

That's the aim! ;)

[@meghasharma5239]

Thankyou mam so much for your efforts

[@ProfessorMdoesScience]

Thanks for watching!

[@Faith-hu3tu]

Hi Professor M, I am wondering why is it important to have a set of compatible observables?

[@ProfessorMdoesScience]

Very good question! This will all become clear when we publish our video on so-called "complete sets of commuting (or compatible) observables". However, let me give you some rough ideas to get started. They key principle is that we are interested in fully characterizing a given quantum system, and the question is: how many observables do we need to fully characterize it? The answer to this is a "complete set of commuting observables". The reason why we use commuting (also called compatible) observables for this is that we can always choose a common set of eigenstates for them, as explained here: kzbin.info/www/bejne/f5mtp4tqfZyroaM In this way, to fully characterize a quantum system we can keep adding compatible observables until we have a full characterization. To give you an example: to fully characterize the hydrogen atom we need at least three mutually commuting observables, and these are typically taken to be the Hamiltonian H (corresponding to the total energy), the squared orbital angular momentum L^2, and the z-component of orbital angular momentum Lz. I hope this helps!

[@Faith-hu3tu]

@@ProfessorMdoesScience Thanks a lot, looking forward to the video!

[@armalify]

Well done.

[@ProfessorMdoesScience]

Thanks!

[@Upgradezz]

Smashed the like button!!

[@ProfessorMdoesScience]

Thanks for your support! :)

[@snjy1619]

🤩🤩🤩🤩