Principles of Quantum Mechanics · Problem 15.1.1

Addition of Angular Momenta — R. Shankar

Physics — Quantum Mechanics · addition-angular-momenta-two-spin-half

Problem

Derive Eqs. (15.1.10) and (15.1.11). It might help to use

\mathbf{S}_1\cdot\mathbf{S}_2 = S_{1z}S_{2z} + \tfrac{1}{2}(S_{1+}S_{2-} + S_{1-}S_{2+}) \tag{15.1.12}