A Modern Approach to Quantum Mechanics · Problem 3.25

Time Evolution — John S. Townsend

Physics — Quantum Mechanics · spin-three-halves-sy-eigenstates

Problem

((a)) Determine the matrix representation for

\hat{S}_y

for a spin-

\frac{3}{2}

particle. ((b)) Determine the normalized eigenstate of

\hat{S}_y

with eigenvalue

\frac{3}{2}\hbar

. ((c)) As noted in Problem 3.22, arsenic atoms in the ground state are spin-

\frac{3}{2}

particles. A beam of arsenic atoms with

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

enters 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