Gauge invariant periodic quantization method

Abstract

Based on the variational principle in a general manifold in the Hilbert space and the principle of gauge invariance, the general gauge invariant periodic quantization method is formulated. This method, which is a direct generalization of the one previously obtained in the case of time-dependent Hartree-Fock, leads to a quantization rule which takes the Bohr-Sommerfeld form when the variational parameters are transformed to canonical variables. The method is illustrated by applying it to the manifold of minimum wave packets for a simple harmonic oscillator. It leads to the exact energy spectrum and a discrete set of wave packets which have maximum overlap with the exact eigenstates. The method is also applied to the exact Schrödinger dynamics where it exposes some open questions of the method.