Question

This may be a bit advanced, but...
How do you calculate eigenfunctions given the spin matrices and their eigenvalues?

Answer 1

I'm just curious but what course are you taking?

Answer 2

@Silent_Sorrow
I am going to assume you are taking non relativistic QM. Its been many many years since I had that course. But let me make a feeble attempt, that if there are no terms in the Hamiltonian that contain both a spin dependence and a coordinate dependence then the eigenfunction can be written as a product of the spin part and the spatial part.
\[\Psi = \phi _{1}(\vec r)\chi _{+}+\phi _{2}(\vec r)\chi _{-}=\left(\begin{matrix}\phi _{1} \\ \phi _{2}\end{matrix}\right)\]

You might try https://www.physicsforums.com/ it is more advanced.

Answer 3

Also my might refer to a specific application in seeking an answer to your issue.