Quantum Mechanics: Concepts and Applications · Problem 7.29

Identical Particles — Nouredine Zettili

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

Problem

Let the Hamiltonian of two nonidentical spin

\frac{1}{2}

particles be

\hat{H} = \frac{\varepsilon_1}{\hbar^2}(\hat{S}_1 + \hat{S}_2)\cdot\hat{S}_1 - \frac{\varepsilon_2}{\hbar}(\hat{S}_{1_z} + \hat{S}_{2_z}),

where

\varepsilon_1

and

\varepsilon_2

are constants having the dimensions of energy. Find the energy levels and their degeneracies.