(a) In the presence of a uniform and static magnetic field B along the z-axis, the Hamiltonian is given by

Solve this problem to obtain the energy levels of all four states using degenerate time-independent perturbation theory (instead of diagonalizing the Hamiltonian matrix). Regard the first and second terms in the expression for H as H₀ and V, respectively. Compare your results with the exact expressions

where triplet (singlet) m = 0 stands for the state that becomes a pure triplet (singlet) with m = 0 as B → 70.

(b) We now attempt to cause transitions (via stimulated emission and absorption) between the two m = 0 states by introducing an osciiiating magnetic field of the "right" frequency. Should we orient the magnetic field along the z-axis or along the x- (or y-) axis? Justify your choice. (The original static field is assumed to be along the z-axis throughout.)

(c) Calculate the eigenvectors to first order.

Transcribed Image Text:

H = AS1. S2 + eB mec (Siz - Szz).