Spin spherical harmonics - Alchetron, the free social encyclopedia

In quantum mechanics, spin spherical harmonics Y_{l, s, j, m} are spinors eigenstates of the total angular momentum operator squared:

j 2 Y l , s , j , m = j ( j + 1 ) Y l , s , j , m j z Y l , s , j , m = m Y l , s , j , m

where j = l + s. They are the natural spinorial analog of vector spherical harmonics.

For spin-1/2 systems, they are given in matrix form by

Y j ± 1 2 , 1 2 , j , m = 1 2 ( j ± 1 2 ) + 1 ( ∓ j ± 1 2 ∓ m + 1 2 Y j ± 1 2 m − 1 2 j ± 1 2 ± m + 1 2 Y j ± 1 2 m + 1 2 )

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