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Recently I have been asked to solve the problem of an electron in a Zeemanfield that couples the spin of the electron to the magnetic field.
I am not sure how to correctly set up the problem. I think, however, that what I have done on the picture is correct. The usual p^2/2m + V term in the Hamiltonian is tensored with the identity matrix and the Zeeman term is added in the usual way.
I am however unsure how to solve this Hamiltonian. How do you solve something like this with both an eigenvalue equation in the matrix structure and in the spatial part of H?
I am not sure how to correctly set up the problem. I think, however, that what I have done on the picture is correct. The usual p^2/2m + V term in the Hamiltonian is tensored with the identity matrix and the Zeeman term is added in the usual way.
I am however unsure how to solve this Hamiltonian. How do you solve something like this with both an eigenvalue equation in the matrix structure and in the spatial part of H?
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