Spherical Tensor Operators | Wigner D-Matrices | Clebsch-Gordan & Wigner-Eckart

[@dy1607]

Spent several classes to learn these stuff. Tough thing. A good video to review.

[@PrettyMuchPhysics]

Thanks for the nice comment!

[@tomsmith6878]

I think this is the first video you guys have done that wasn't covered in my degree (ive watched most of them)… nice work!

[@PrettyMuchPhysics]

We encountered them in a QM course, when talking about the Wigner-Eckart theorem. But also really nothing more than „they exist“. So we wanted to find out what spherical tensors are, how to use them and so on.

[@tomsmith6878]

@@PrettyMuchPhysics same here, we covered Wigner Eckart without mentioning these

[@surbhisinha8959]

You guys are the best. Thank you 🥺

[@PrettyMuchPhysics]

:)))

[@luanmartins8068]

although the video is a bit fast, it's very well explained and clarified a lot of things, and also the way the notations were done was splendid!

[@PrettyMuchPhysics]

Thank you very much! :)

[@mdshaifullah9598]

Awesome channel. I love this channel so far. I would have been better if you made a tensor series for physics students.

[@park19970429]

I’m very moved with your kind explanation! Thank you so much!!

[@PrettyMuchPhysics]

Thank you for your nice comment! :)

[@ИгорьДымченко-к9л]

Absolutely Great explanation.

[@PrettyMuchPhysics]

Thank you very much!

[@paintokk799]

Thank you for wonderful explaination! I am wondering how to obtain the tranformation of spherical harmonics under rotations (Y_{lm} --> D_{R}^{\dagger} Y_{lm} D_{R}) at 8:06. There is a bit leap from the previous derivation.

[@gerardotoscano8090]

Hory shit ma man, this is incredible, ive finally understood QM in an easy and condensed way, i´ve been trying to understend these topics for months and even tho i did in a reasonable amount, now i understand so clear what is going on, Thank you so much, seriously. PD. I hope in the future you get interested in explaining some of the Judd Ofelt theory, specially, the combination of two tensor operators (dipole moment operator and Crystal field operator) into one using the 3j wiegner symbols. But it is just a hope. Anyway, I'll have donate soon cos this is amazing.

[@PrettyMuchPhysics]

Thank you very much for your kind comment! :) TBH, I haven't heard of Judd-Ofelt theory until now, but it looks interesting! By the way, we did two videos on the Wigner-j symbols: kzbin.info/www/bejne/q5moo5J4d8aCkLs and kzbin.info/www/bejne/pIqcYY2hYsSkp6s 🙂

[@gerardotoscano8090]

@@PrettyMuchPhysics Yeah, thank you very much, im actually watching them right now

[@mergen9802]

7:10 why is it J that enters D=exp(-i θ J)? Does it also include spin degree of freedom?

[@PrettyMuchPhysics]

We used J to denote the generator of rotations in general. If there is no spin in your system, then the generator of rotations is L.

[@mergen9802]

@@PrettyMuchPhysics what if there is a spin d.o.f.? Would it be the total J instead of L? Naively I would assume it's still L since R is a spatial rotation...

[@정웅찬-p8s]

thanks for making this video! but i have a question 4:25, coefficient of spherical basis. e+ and e- inner product is 0 when alpha=1/2, beta=1/2 why are alpha and beta's sign differently?

[@thenaughty5441]

Wow this is so helpful, thankyou !

[@PrettyMuchPhysics]

We're glad it was useful to you! 😃

[@DarkRanger882046]

Thanks. great job.

[@PrettyMuchPhysics]

Thank you! 😁

[@MastermindofBCB]

Very nice work! May I ask what Soft-/Hardware you use as a "blackboard". Need to give some online exercises this semester and I'm somehow not very pleased with the stuff we have.

[@PrettyMuchPhysics]

Thanks! Software: "Explain Everything", hardware: iPad + Apple Pencil!

[@adonaihilario1006]

Using the relation shown in 13:50 I can write Y_(1,0) = Y_(1,-1) Y_(1,1) ⟨1 -1 1 1 | 1 0⟩ + Y_(1,-1) Y_(1,-1) ⟨1 1 1 -1 | 1 0⟩ but this yields zero, while it should yield Y_(1,0) = sqrt(3/4π) cos(θ). What am I doing wrong here?

[@PrettyMuchPhysics]

The second line with Y_LM etc. should have been under quotation marks or something; it's more symbolical and we should have made this more clear, I'm sorry. Two spherical harmonics contract like this: en.wikipedia.org/wiki/Spherical_harmonics#Contraction_rule and the reason is explained here: physics.stackexchange.com/questions/512197/decomposition-of-spherical-harmonics-via-clebsh-gordan-coefficients

[@krishanusengupta7710]

Thanks a lot.

[@ngankinfung]

I think the CGC table is lacking some square root?

[@PrettyMuchPhysics]

Yes, exactly! Usually, in order to save space, square roots are omitted from Clebsch-Gordan tables. So if you see a „-1/3“, this actually means „-sqrt(1/3)“!

[@ngankinfung]

@@PrettyMuchPhysics Great video anyway!

[@PrettyMuchPhysics]

Thanks :D

[@devangshukla3688]

Pretty nice

[@PrettyMuchPhysics]

Thanks!

[@taw3e8]

well... that's not my level :(

[@PrettyMuchPhysics]

Doesn't have to be! Remember, our videos are meant to be a refresher when you study something and don't quite understand it. No need to worry if you don't understand such a topic after the first watch!

[@taw3e8]

@@PrettyMuchPhysics well, i'll have to study it first to be able to refresh it...

[@PrettyMuchPhysics]

@@taw3e8 Exactly! And if you do, please come back and rewatch it :D

[@taw3e8]

@@PrettyMuchPhysics i'm sure i'll be back :p

[@Ovechkin8484]

Fuck yeah

[@PrettyMuchPhysics]

:D

[@jakubjungle656]

A man in a dream told me that you could use the framework of angular momentum and spherical resonance as a cypher for non-commutative, quasi linear fluid dynamics. The cypher decodes all the way down to a singular non-tensosorial expression which defines itself as "the absolute zero of space-time" . A sub quantum VOID which pulls time in one side and spits out the other like a black hole but with no gravity.

[@jakubjungle656]

The time that spits out from this void, is observable and measurable. The quantum foam is the residue of the past, as it passes time along, it blends the consequences of the previous moment and applied them generously to the eventualities and inevitabilities of the future, from one moment onto the next, for ever. Until some military learns how to split it like an atom cuz that would probably kill us all.