Robert Mann - An Introduction to Particle Physics and the Standard Model · Problem 5.4

Accelerators — Robert Mann

Physics — Particle Physics · angular-momentum-commutators

Problem

Consider the Hamiltonian

H = H_0 - g\frac{\mu_0}{\hbar}\vec{J} \cdot \vec{B}

where

\vec{B}

is an external magnetic field,

g, \mu_0

are constants, and

H_0

commutes with the angular momentum operator

\vec{J}

. If the magnetic field is pointing along the

z

-axis, find the commutator

\left[H, \vec{J}\right]