Gauge transformations in nonrelativistic quantum mechanics and different forms of the photon–electron interaction

Abstract

The properties of the Schrödinger equation under electromagnetic gauge transformations are investigated. A procedure to obtain gauge-invariant matrix elements and transition probabilities within perturbation theory is pointed out. Using this formalism, it is shown that the two commonly used photon–electron interaction Hamiltonians denoted as p∙A and r∙E cannot be connected by a gauge transformation and are therefore not necessarily equivalent. The conclusions are illustrated by an example from multiphoton ionization in strong radiation fields.