Hi, for my quantum mechanics course I'm confronted with the following question: 1. The problem statement, all variables and given/known data A spin 1/2 particle has the following eigenstates of Sz: |+> = (1 0) and |-> = (0 1). A magnetic field is pointing in the z direction, B = (0,0,B). The Hamiltonian is H = -B * n, with n = -(e/mc)S and S = h/4pi * s (with B, n, S, and s vectors and H of course an operator). The questions are a) to find the normalized energy eigenstates and eigenvalues and b) to find the normalized eigenstates and eigenvalues of Sx in terms of the eigenstates of Sz. 2. Relevant equations The Pauli spin matrices are most important here, for a) only the z component is relevant as the magnetic field only has a z component and the Hamiltonian is defined as -B * n. For b) I think the x component is also relevant. sz= (1 0) (0 -1) sx= (1 0) (0 1) 3. The attempt at a solution I think I got the most far on question a). I calculated H and found it to be H = (ehB/4pi*mc)* (1 0) (0 -1) Then, using the determinant of (H - lambda * I) I calculated the eigenvalues of H: lambda = +/- (ehB/4pi*mc). After that, I used the eigenvalue equation Av = lambda*v to find the eigenvectors (1 0) and (0 1). I don't think that should be surprising though because somewhere in the book (Introductory Quantum Mechanics by Liboff) it says that Sz and H have the same eigenfunctions. But are these normalized? And are these values/vectors correct? On question b) I don't really know what to do - if I try finding out the eigenstates of Sx I get stuck on the vectors. I get equations like h/4pi (b a) = (a b) which doesn't have a solution except for a = b = 0 which obviously is incorrect. How do I find the correct eigenstates? And how do I then find out how to write them as combinations of eigenstates of Sz? Hope someone can help!