Franz Schwabl Quantum Mechanics 4th Edit · Problem 10.2

Approximation Methods for Stationary States

Physics — Quantum Mechanics · spin-half-two-particle-energy-eigenvalues

Problem

Suppose that a system consists of two distinguishable particles each with spin

S = 1/2

and is described by the Hamiltonian

H = -\frac{a+b}{2}\,(S_{1,z} + S_{2,z})\,B - \frac{a-b}{2}\,(S_{1,z} - S_{2,z})\,B + J\mathbf{S}_1 \cdot \mathbf{S}_2 \;,

where

a

b

, and

J

are constants, and

B

represents the external magnetic field. Determine the energy eigenvalues.