
#1
Nov2512, 10:34 AM

P: 4

What are the eigenfunctions of the spin operators? I know the spin operators are given by Pauli matricies (https://en.wikipedia.org/wiki/Spin_o...lation_of_spin), and I know what the eigenvalues are (and the eigenvectors), but I have no idea what the eigenfunctions of the spin operator are. I searched google but I could not find a derivation. Does anyone know how to find the eigenfunctions of the spin operator?




#2
Nov2512, 11:19 AM

Sci Advisor
Thanks
P: 3,861

Do you mean spin spherical harmonics? These are the functions that represent finite rotations in spin space, halfinteger analogs to the Y_{lm}'s. They're briefly mentioned in Wikipedia, covered more in this article, and especially in books on angular momentum, like the monograph by Edmonds.




#3
Nov2512, 11:40 AM

P: 4

Like the Pauli matricies Sx, Sy, Sz, I know the eigenvalues/eigenvectors, but what are the eigenfunctions? I have no idea what they could be.




#4
Nov2512, 12:02 PM

Sci Advisor
HW Helper
P: 11,866

eigenfunctions of spin operator
The spin space is an abstract finite dimensional (essentially C^(2s+1)) vector space. There are no <wavefunctions>, just normal quadratic matrices and matrices with one column.




#5
Nov2512, 01:01 PM

Sci Advisor
Thanks
P: 3,861




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