# Coupling of angular momenta

#### Dreak

Hello, I have a small question about coupling of angular momenta.

When you have JÂ² with J = J1 + J2; you change it to the form (dropping the hbar in all equations):

jÂ² = j1Â² + j2Â² + j1-j2+ + j1+j2- + 2j1zj2z

now it's these j1-j2+ I have a problem with.

Let's say you use it on |1/2;-1/2>. The answer is âˆš[j1(j1+1) - m1(m1-1)] . âˆš[j2(j2+1) - m2(m2 + 1)]

Ok, no problem. But apperently, the answer is: âˆš[1/2(1/2+1) - 1/2(1/2-1)] . âˆš [ 1/2(1/2 + 1) - (-1/2)(-1/2 + 1)]

So the j2 = 1/2 and not -1/2 and I don't know why...
Unless it is because the angular momenta is quantisised from 0, 1, ...? Could that be it?
and what if you a further j- on the new basecomponent?

edit: nvm, found out :)

Last edited:
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#### DrClaude

Mentor
Let's say you use it on |1/2;-1/2>
That notation is a shorthand for $| m_1; m_2 \rangle$, where it is assumed that these are spin-1/2 particles, $j_1 = j_2 = 1/2$.

"Coupling of angular momenta"

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