A Modern Approach to Quantum Mechanics · Problem 3.14

Angular Momentum — John S. Townsend

Physics — Quantum Mechanics · spin-1-matrix-representations

Problem

Derive the

3\times 3

matrix representations of

J_x

J_y

, and

J_z

for a spin-1 (

j=1

) particle using the states

|1,1\rangle

|1,0\rangle

, and

|1,-1\rangle

as a basis, by using the matrix elements of the raising and lowering operators (3.61) and (3.62).