Coupling of angular momenta

  • Thread starter Dreak
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Hello, I have a small question about coupling of angular momenta.

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

j² = j1² + j2² + 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 √[j1(j1+1) - m1(m1-1)] . √[j2(j2+1) - m2(m2 + 1)]

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


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##.

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