A Modern Approach to Quantum Mechanics · Problem 4.8

A System of Two Spin-1/2 Particles — John S. Townsend

Physics — Quantum Mechanics · spin-half-constant-magnetic-field-time-evolution

Problem

A spin-

\frac{1}{2}

particle, initially in a state with

S_n = \hbar/2

with

\mathbf{n} = \sin\theta\, \mathbf{i} + \cos\theta\, \mathbf{k}

, is in a constant magnetic field

B_0

in the

z

direction. Determine the state of the particle at time

t

and determine how

\langle S_x\rangle

\langle S_y\rangle

, and

\langle S_z\rangle

vary with time.