Consider a spin 23 particle whose Hamiltonian is given by
H^=ℏ2ε0(S^x2−S^y2)−ℏ2ε0S^z2,
where ε0 is a constant having the dimensions of energy.
(a) Find the matrix of the Hamiltonian and diagonalize it to find the energy levels.
(b) Find the eigenvectors and verify that the energy levels are doubly degenerate.