1. The problem statement, all variables and given/known data Consider a spin system with noninteracting spin 1/2 particles. The magnetic moment of the system is written as: μ = (ħq/2mc)σ Where σ = (σx, σy, σz) is the Pauli spin operator of the particle. A magnetic field of strength Bz is applied along the z direction and a second field Bx is applied along the x direction. The Hamiltonian of the particles is: H = H0 + V H0 = -μzBz V = -μxBx a) Find the eigenvalues and eigenkets of H0 b) Express V in terms of σ+ and σ- c) Find the eigenvalues and eigenkets of H 2. Relevant equations σ+ = σx + iσy σ- = σx - iσy σ+ = |+><-| σ- = |-><+| σz|+> = 1|+> σz|-> = -1|-> 3. The attempt at a solution For part a) I'm pretty sure I did it right H0 = (-qBzħ/2mc)σz or H0 = ε0σz if ε0 = -qBzħ/2mc. The operators H0 and σz commute so they have the same eigenkets |+> and |-> Using the expression for H0 and the eigenvalue equations for σz given above the eigenkets of H0 are ε0 and -ε0. Part b I'm not so sure. I wrote the expression for V in the same way that I did for H0: V = (-qBxħ/2mc)σx Then using equations given above I worked out that σx = (σ+ + σ-)/2, so I subbed that into the the expression to get: V = (-qBxħ/4mc)(σ+ + σ-) When I try to do part c I start running into problems and I think it is because I did something in part a or b wrong. Can anyone tell me if I've made any mistakes in part a or b?