Time evolution of spin
Discuss the following:
Consider a spin 1/2 particle placed in a magnetic field Bowith components
{Bx=Bo/√2
By=0
Bz=Bo/√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.