Introduction to Quantum Mechanics · Problem 4.37

Quantum Mechanics in Three Dimensions — David J. Griffiths

Physics — Quantum Mechanics · addition_angular_momenta

Problem

(a) Apply

S_-

|1\,0\rangle

(Equation 4.175), and confirm that you get

\sqrt{2}\hbar\,|1\,-1\rangle

. (b) Apply

S_\pm

|0\,0\rangle

(Equation 4.176), and confirm that you get zero. (c) Show that

|1\,1\rangle

and

|1\,-1\rangle

(Equation 4.175) are eigenstates of

S^2

, with the appropriate eigenvalue.