Recently I have been asked to solve the problem of an electron in a Zeeman-field 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?