Consider a particle of spin s=3/2.
(a) Find the matrices representing the operators S^z, S^x, S^y, S^x2, and S^y2 within the basis of S^2 and S^z.
(b) Find the energy levels of this particle when its Hamiltonian is given by
H^=ℏ2ε0(S^x2−S^y2)−ℏε0S^z,
where ε0 is a constant having the dimensions of energy. Are these levels degenerate?
(c) If the system was initially in an eigenstate ∣ψ0⟩=1000, find the state of the system at time t.