Quantum Mechanics: Concepts and Applications · Problem 7.30

Identical Particles — Nouredine Zettili

Physics — Quantum Mechanics · spin-hamiltonian-energy-levels

Problem

Find the energy levels and their degeneracies for a system of two nonidentical spin

\frac{1}{2}

particles with Hamiltonian

\hat{H} = \frac{\varepsilon_0}{\hbar^2}(\hat{S}_1^2 + \hat{S}_2^2) - \frac{\varepsilon_0}{\hbar}(\hat{S}_{1_z} + \hat{S}_{2_z}),

where

\varepsilon_0

is a constant having the dimensions of energy.