A Modern Approach to Quantum Mechanics · Problem 4.15

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

Physics — Quantum Mechanics · spin-3-half-hamiltonian-sx

Problem

If the Hamiltonian for a spin-

\frac{3}{2}

particle is given by

\hat{H} = \omega_0 \hat{S}_x

and at time

t = 0

|\psi(0)\rangle = |\frac{3}{2}, \frac{3}{2}\rangle

, determine the probability that the particle is in the state

|\frac{3}{2}, -\frac{3}{2}\rangle

at time

t

. Evaluate this probability when

t = \pi/\omega_0

and explain your result. Suggestion: See Problem 3.23 for the eigenstates of

\hat{S}_x