Gauge Invariance in non-relativistic quantum mechanics

Summary

We show that non-relativistic quantum mechanics is invariant under a local gauge transformation even in the absence of any external electromagnetic field, provided we do not exclude the arbitrary phase factor in the coordinate representation of the wave vector. A generalised, gauge-invariant form of the Schroedinger equation, as well as gauge-invariant canonical momentum and Hamiltonian operators are introduced. In the presence of an electromagnetic field, the new Hamiltonian operator turns out to be identical with the «energy operator» introduced by K. H. Yang. A previously derived result, proving thenon-equivalence of the minimal-coupling and the multipolar forms of matter-radiation interaction, is shown to follow as a corollary.