A Modern Approach to Quantum Mechanics · Problem 1.2

Rotation of Basis States and Matrix Mechanics — John S. Townsend

Physics — Quantum Mechanics · magnetic-moment-angular-momentum

Problem

Show for a solid spherical ball of mass

m

rotating about an axis through its center with a charge

q

uniformly distributed on the surface of the ball that the magnetic moment

\boldsymbol{\mu}

is related to the angular momentum

\mathbf{L}

by the relation

\boldsymbol{\mu} = \frac{5q}{6mc}\mathbf{L}

Reminder: The factor of

c

is a consequence of our using Gaussian units. If you work in SI units, just add the

c

in by hand to compare with this result.