Principles of Quantum Mechanics · Problem 20.6

The Dirac Equation — R. Shankar

Physics — Quantum Mechanics · dirac-equation-spin

Problem

Show that the orbital angular momentum

\mathbf{L}

is not conserved for a free Dirac particle but that the total angular momentum

\mathbf{J} = \mathbf{L} + \frac{1}{2}\hbar\boldsymbol{\Sigma}

is conserved, where

\boldsymbol{\Sigma} = \begin{pmatrix} \boldsymbol{\sigma} & 0 \\ 0 & \boldsymbol{\sigma} \end{pmatrix}.