Principles of Quantum Mechanics · Problem 15.2.1

Addition of Angular Momenta — R. Shankar

Physics — Quantum Mechanics · clebsch-gordan-angular-momentum

Problem

(1) Verify that

|j_1 j_1, j_2 j_2\rangle

is indeed a state of

j = j_1 + j_2

by letting

J^2 = J_1^2 + J_2^2 + 2J_{1z}J_{2z} + J_{1-}J_{2+} + J_{1+}J_{2-}

act on it. (2) (optional) Verify that the right-hand side of Eq. (15.2.8) indeed has angular momentum

j = j_1 + j_2 - 1