A Modern Approach to Quantum Mechanics · Problem 4.12

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

Physics — Quantum Mechanics · spin-1-magnetic-field-x-direction

Problem

A particle with intrinsic spin one is placed in a constant external magnetic field

B_0

in the

x

direction. The initial spin state of the particle is

|\psi(0)\rangle = |1, 1\rangle

, that is, a state with

S_z = \hbar

. Take the spin Hamiltonian to be

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

and determine the probability that the particle is in the state

|1, -1\rangle

at time

t

. Suggestion: If you haven't already done so, you should first work out Problem 3.15 to determine the eigenstates of

\hat{S}_x

for a spin-1 particle in terms of the eigenstates of

\hat{S}_z