@@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!
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〉?
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 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.
Thx! Perfect timing! Writing a quantum mechanics exam on Wednesday :)
That‘s awesome, good luck!
@@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!
That‘s great, congratulations! 🎉
Really easy to follow, amazing work from you all as always!
Thank you very much for your nice comment!
Wonderfully explained, guys!
Thank you Parth 😊
this came up by the time i started Atomic physics! thank you so much!
:D Thanks for watching!
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〉?
ayo, mah man, great explanation but where's the reduced planck's constant @3:27 ?
Amazing video! Thank you very much!
In general for n particles of spin s How many entries of the matrix will be zero?
Sir, which software do you use for writing?
It’s an iPad app called „Explain Everything“!
Thank you!
Glad you liked it :)
Afraid I don't recognize the symbol you have used @ 3:40
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>
at 4:33, why gamma 1 = gamma 2 ? can anyone explain>?
is it because [10> is an eigenstate of J^2?
@@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.