Do not stop, you make really good and understandable videos, it would be better if you will solve some problems as examples for more understanding. Thanks for your work
Glad you like the videos, and thanks for the suggestion! We are preparing some extra resources to go with the videos, including problems+solutions, we'll hopefully make an announcement soon!
Fantastic explanation! When I subscribed the channel, there were only a few hundred subs. Now there are 6.56k ! You deserve more applauses than this. Hope it keeps growing.
Fantastic Derivation I really like the using m=l and using that to find a basic relation. However it adds some work to calculate for general m. Having to recalculate normalization constant and then putting l=m wherever required will give general expression. But hey its a lot better than three confusing methods from Zettili
Hi! Your videos really helped me clear my concepts of orbital angular momentum. Thank you so much for posting such videos. At the same time, it is an earnest request to post similar videos on spin angular momentum as well. Thanks!
Dear Prof M, where in the complete Spherical Harmonics Equation comes these factors from: Sq root ((l+m)!/(l-m)!) and the cosine derivative at the end respect to (sin(theta)^2l)
Thanks for the excellent video! Can you explain why the raising and lowering operators preserve normalisation though? You mentioned this at 11:34 but it seems to me that since they are not unitary, they do not preserve normalisation.
Thanks for the question, and let me clarify what we mean. The general properties of the angular momentum ladder operators are described in this video: th-cam.com/video/yGvfqRfw1BE/w-d-xo.html In that video, we show that for normalised states |l,m> and |l,m-1>, then the action of the lowering operator is: L- |l,m> = hbar*sqrt[l(l+1)-m(m-1)] |l,m-1> (note that in the video on ladder operators we actually use the general angular momentum J and the eigenvalues are labelled lambda and mu, but you can go to the especific form for orbital angular momentum using the replacements J --> L, lambda --> hbar^2*l(l+1) and mu --> hbar*m). In this step you are describing, we use the correct prefactor such that the states |l,m> and |l,m-1> are therefore each properly normalized. I hope this helps!
Do not stop, you make really good and understandable videos, it would be better if you will solve some problems as examples for more understanding. Thanks for your work
Glad you like the videos, and thanks for the suggestion! We are preparing some extra resources to go with the videos, including problems+solutions, we'll hopefully make an announcement soon!
Best channel for quantum mechanics....🙏
Glad you like it! :)
I am self learning QM and your videos are incredibly helpful. Thank you and please continue the good work!
Great to hear they are useful, and good luck in your learning journey!
This is some intense brain gym. Thanks!
Hope it is helpful! :)
Thank you for this elegant work!!!
Thanks for watching! :)
Fantastic explanation! When I subscribed the channel, there were only a few hundred subs. Now there are 6.56k ! You deserve more applauses than this. Hope it keeps growing.
Wow, thanks for your continued support!! :)
Fantastic Derivation
I really like the using m=l and using that to find a basic relation. However it adds some work to calculate for general m. Having to recalculate normalization constant and then putting l=m wherever required will give general expression.
But hey its a lot better than three confusing methods from Zettili
There are indeed quite a few ways to get to the final expressions, and glad to hear our approach was clear! :)
Some of the best content out there! I am so grateful for your videos!
- An Undergraduate Mathematics student.
Glad you like the videos! May we ask where you study?
@@ProfessorMdoesScience Hi I sent you an email about referencing your videos :)
@@harrisonbennett7122 Ups, somehow missed that; we have responded now! :)
Hi! Your videos really helped me clear my concepts of orbital angular momentum. Thank you so much for posting such videos. At the same time, it is an earnest request to post similar videos on spin angular momentum as well. Thanks!
Glad it helped! And we are about to start a new series looking at spin angular momentum for spin-1/2 particles, so stay tuned! :)
Again, thank you!! Excellent!
Thanks for watching! :)
😊😊😊😊 Please give the spin angular momentum playlist
Hoping to get there soon!
Dear Prof M, where in the complete Spherical Harmonics Equation comes these factors from: Sq root ((l+m)!/(l-m)!) and the cosine derivative at the end respect to (sin(theta)^2l)
Thanks for the excellent video! Can you explain why the raising and lowering operators preserve normalisation though? You mentioned this at 11:34 but it seems to me that since they are not unitary, they do not preserve normalisation.
Thanks for the question, and let me clarify what we mean. The general properties of the angular momentum ladder operators are described in this video: th-cam.com/video/yGvfqRfw1BE/w-d-xo.html
In that video, we show that for normalised states |l,m> and |l,m-1>, then the action of the lowering operator is:
L- |l,m> = hbar*sqrt[l(l+1)-m(m-1)] |l,m-1>
(note that in the video on ladder operators we actually use the general angular momentum J and the eigenvalues are labelled lambda and mu, but you can go to the especific form for orbital angular momentum using the replacements J --> L, lambda --> hbar^2*l(l+1) and mu --> hbar*m). In this step you are describing, we use the correct prefactor such that the states |l,m> and |l,m-1> are therefore each properly normalized. I hope this helps!
Thanks a lot but sometimes I just find it a bit hard to understand your handwriting.
Thanks for the feedback! What aspect do you find hard to understand? The text or the formulas? Something specific?