Quantum Addition of Angular Momentum in Python: Obtaining the Clebsch-Gordan Coefficients

In this video I use the python module sympy to explore quantum addition of angular momentum and obtain the Clebsch-Gordan coefficients. Examined, for example, is the use of tensor products to construct appropriate operators.
All code for this video can be found on my github:
github.com/lukepolson/youtube...
Come hang out the discord server:
/ discord

[@PrettyMuchPhysics]

Great video! Seeing all these matrices explicitly is much more instructive than only using symbolic notation 👍

[@TheDavddd]

This is way better explained than any lecture I've seen on the subject.

[@MrPSolver]

Thank you! It's not easy material...I still don't know if I'm 100% satisfied with my description of it either

[@TheHulkNorris]

I'm looking forward to seeing an album with all your best songs :)

[@timuralmabetov2213]

So underrated channel!

[@greggrieves6950]

Very cool. I was expecting you to just crank out all permutations of recursion relations, but ultimately that would be no more instructive than just reading tables. Here you've let the machine handle the gory details and lets you focus on using the result.

[@MrPSolver]

CORRECTION: I have stated that because S^2 and Sz commute, the share a common eigenbasis. This is false: it is only true if they both have non-degenerate eigenbases (i.e. two eigenvectors don't share the same eigenvalue). It's just a coincidence that sympy's solver gives eigenvectors of S^2 that also happen to be eigenvectors of Sz (might have to do with the fact that Sz is diagonal). To do this more rigorously, one should use qutip.org/docs/latest/modules/qutip/simdiag.html

[@MM-vw1ck]

Great video, as always, tbh I liked the previous UI a bit more.

[@hsh7677]

Amazing 🤩

[@ameerbaloch9894]

amazing

[@thanglexuan8837]

cool, bro.

[@ShinjiCarlos]

Hey, Luke! Nice content and mission! I was wondering: what about explore a litle bit of Qutip - a Python library with tons of stuff to deal with some advanced topics in Quantum Mechanics?

[@user-kw5rp9vx2u]

Great content! Can you please do a video on pdes?

[@luismaman9236]

Awesome video but I liked the old setup more

[@user-er1lo1hj4x]

Hello..I am a PhD student in physics from Iraq..I hope you can help me find codes in the Python program to study the Fe(II)particle (ising model 2D)to determine the spin crossover of the electrons and find the energy..with many thanks to you.

[@bekarysbereketov4515]

Hello.I am undergraduate student. i am doing diploma work and i stuck.
Could you help me write down code for finding angular momentum and spin of the nuclei)

[@alabamacajun7791]

Less music is better, Lie Algebra is loud enough.