  By using the multipolar gauge it is shown that the quantum mechanics of an
electrically charged particle moving in a prescribed classical electromagnetic
field (wave mechanics) may be expressed in a manner that is gauge invariant,
except that the only gauge functions that are allowable in a gauge
transformation are those that consist of the sum of a function that depends
only on the space coordinates and a term that is the product of a constant and
the time coordinate. The multipolar gauge specifies the specific set of
potentials that are best suited for use in the Schroedinger equation.
