A Modern Approach to Quantum Mechanics · Problem 1.5

Rotation of Basis States and Matrix Mechanics — John S. Townsend

Physics — Quantum Mechanics · spin-half-sy-amplitude

Problem

(a) What is the amplitude to find a particle that is in the state

|{+}\mathbf{n}\rangle

(from Problem 1.3) with

S_y = \hbar/2

? What is the probability? Check your result by evaluating the probability for an appropriate choice of the angles

\theta

and

\phi

. (b) What is the amplitude to find a particle that is in the state

|{+}\mathbf{y}\rangle

with

S_n = \hbar/2

? What is the probability?