A. Zee, Quantum Field Theory in a Nutshell · Problem III.5.1

Field Theory Redux

Physics — QFT

Problem

Obtain the Klein-Gordon equation for a particle in an electrostatic potential (such as that of the nucleus) by the gauge principle of replacing

(\partial/\partial t)

in (2) by

\partial/\partial t - ieA_0

. Show that in the nonrelativistic limit this reduces to the Schrödinger's equation for a particle in an external potential.