Discuss hamiltonian of the system

Question

Time evolution of spin

Discuss the following:

Consider a spin 1/2 particle placed in a magnetic field Bowith components

{B_x=B_o/√2
 B_y=0
B_z=B_o/√2}

(a) Calculate the matrix representing in the { | + >, | - > } basis, the operator H, the Hamiltonian of the system.

(b) Calculate the eigenvalues of H

(c) The system at the time t = 0 is in the state | _ >. What values can be found if the energy is measured, and with what probabilities?

(d) Calculate the state vector at time t. At this instant, S, is measured; what is the mean value of the reuslts that can be obtained? Give a geometrical interpretation.