Quantum Mechanics: Concepts and Applications · Problem 7.31

Identical Particles — Nouredine Zettili

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

Problem

Consider two nonidentical spin

s = \frac{1}{2}

particles with Hamiltonian

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

where

\varepsilon_0

is a constant having the dimensions of energy. Find the energy levels and their degeneracies.