A Modern Approach to Quantum Mechanics · Problem 3.22

Time Evolution — John S. Townsend

Physics — Quantum Mechanics · spin-three-halves-stern-gerlach

Problem

Arsenic atoms in the ground state are spin-

\frac{3}{2}

particles. A beam of arsenic atoms enters an SGx device, a Stern–Gerlach device with its inhomogeneous magnetic field oriented in the

x

direction. Atoms with

S_x = \frac{1}{2}\hbar

then enter an SGz device. Determine the fraction of the atoms that exit the SGz device with

S_z = \frac{3}{2}\hbar

S_z = \frac{1}{2}\hbar

S_z = -\frac{1}{2}\hbar

, and

S_z = -\frac{3}{2}\hbar