Energy variational principle and charge conservation for a many-particle system in a magnetic field

Abstract

When the energy variational principle is applied to a many-particle system in a magnetic field, the trial wave function is generally chosen without regard to the gauge used for the vector potential. This procedure leads to gauge-dependent energy expectation values and charge nonconservation. By mutiplying the trial wave function by a phase factor with a spatially dependent phase function and varying the energy expectation value with respect to the phase function, the charge conservation condition is obtained and a gauge-invariant energy expectation value results.