Principles of Quantum Mechanics · Problem 20.10

The Dirac Equation — R. Shankar

Physics — Quantum Mechanics · dirac-equation-nonrelativistic-limit

Problem

Starting from the Dirac equation for a particle in an electromagnetic field, derive the Pauli equation in the nonrelativistic limit:

i\hbar\frac{\partial \phi}{\partial t} = \left[\frac{1}{2m}\left(\mathbf{p} - e\mathbf{A}\right)^2 + e\phi - \frac{e\hbar}{2m}\boldsymbol{\sigma}\cdot\mathbf{B}\right]\phi

and show that the

g

-factor of the electron is predicted to be exactly 2.