Deriving Clebsch-Gordan Coefficients | Angular Momentum in Quantum Mechanics

[@ParthGChannel]

Wonderfully explained, guys!

[@PrettyMuchPhysics]

Thank you Parth 😊

[@wernerheisenberg7192]

Thx! Perfect timing! Writing a quantum mechanics exam on Wednesday :)

[@PrettyMuchPhysics]

That‘s awesome, good luck!

[@wernerheisenberg7192]

@@PrettyMuchPhysics haha thanks, mate! I got the result today and it‘s a 1.0 which is the highest grade here in Germany. I actually didn‘t need the CG-coefficients in the exam but your video helped me to be prepared when there would have been an exercise about this (we derived it for Spin-1/2 in homework). Thus you gave me confidence! Thank you! Keep your work up!

[@PrettyMuchPhysics]

That‘s great, congratulations! 🎉

[@ICatPatrol]

Really easy to follow, amazing work from you all as always!

[@PrettyMuchPhysics]

Thank you very much for your nice comment!

[@ΘεόδωροςΜπίκος-υ1ο]

this came up by the time i started Atomic physics! thank you so much!

[@PrettyMuchPhysics]

:D Thanks for watching!

[@giannakos4081]

Amazing video! Thank you very much!

[@meetghelani5222]

ayo, mah man, great explanation but where's the reduced planck's constant @3:27 ?

[@jonathan3372]

I have some questions about the tensor product: (1) At 3:50, why is the middle term 2*(j_1 ⋅ j_2) instead of 2*(j_1 ⊗ j_2)? (I confess I am a bit lost on which of the operators on that page are vectors, scalars, or tensors :/ ) (2) A more general question, is ⊗ commutative for states in Hilbert spaces, e.g. is |state 1〉 ⊗ |state 2〉 the same as |state 2〉 ⊗ |state 1〉?

[@mohammadarshadpathan490]

In general for n particles of spin s How many entries of the matrix will be zero?

[@asifzaman3503]

Sir, which software do you use for writing?

[@PrettyMuchPhysics]

It’s an iPad app called „Explain Everything“!

[@marcossilvadepaula7753]

Thank you!

[@PrettyMuchPhysics]

Glad you liked it :)

[@gerontius1726]

Afraid I don't recognize the symbol you have used @ 3:40

[@PrettyMuchPhysics]

This is a tensor product: ⊗ You could write for example j_1z |j1 m1 j2 m2> but to make it clear what's happening, you can use the tensor product: j_1z ⊗ 1_2 |j1 m1 j2 m2> = j_1z ⊗ 1_2 |j1 m1> ⊗ |j2 m2> = ( j_1z |j1 m1> ) ⊗ ( 1_2 |j2 m2> ) = ( m1 |j1 m1> ) ⊗ ( |j2 m2> ) = m1 |j1 m1 j2 m2>

[@priteshsrivastava5850]

at 4:33, why gamma 1 = gamma 2 ? can anyone explain>?

[@priteshsrivastava5850]

is it because [10> is an eigenstate of J^2?

[@PrettyMuchPhysics]

@@priteshsrivastava5850 Good question! If you compare coefficients, then you get two equations: (1) g2 + g3 = 2 g2 (2) g2 + g3 = 2 g3 The solution to this set of equations is g2 = g3.