Quantum Mechanics: Concepts and Applications · Problem 5.4

Angular Momentum — Nouredine Zettili

Physics — Quantum Mechanics · spin-energy-levels

Problem

Find the energy levels of a spin

s = \frac{3}{2}

particle whose Hamiltonian is given by

\hat{H} = \frac{\alpha}{\hbar^2}(\hat{S}_x^2 + \hat{S}_y^2 - 2\hat{S}_z^2) - \frac{\beta}{\hbar}\hat{S}_z;

\alpha

and

\beta

are constants. Are these levels degenerate?