(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An electron in a hydrogen atom is in the n = 2, l = 1 state. It experiences a spin-orbit interaction [itex]H' = \alpha \mathbf{L} \cdot \mathbf{S}[/itex]. Calculate the energy level shifts due to the spin-orbit interaction.

2. Relevant equations

Degenerate perturbation theory.

3. The attempt at a solution

This n,l state is triply degenerate due to the three possible values of m = -1,0,1.

The unperturbed Hamiltonian is just what goes in the Schrodinger equation right? In which case the eigenfunctions of the unperturbed hamiltonian are just the spherical harmonics [itex]Y_{lm}[/itex] multiplied by strictly radial functions. So I put

[itex]\psi^{(0)} = \alpha Y_{10} + \beta Y_{1-1} + \gamma Y_{11}[/itex]

So I then write down the matrix [itex] \langle Y_{1,i} |H'| Y_{1,j} \rangle[/itex] and find the eigenvalues.

Am I getting warm?

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# Homework Help: Spin-orbit coupling perturbation

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