Perturbation method beyond the variational Gaussian approximation: The Liouville - von Neumann approach

Abstract

We have developed a variational perturbation theory based on the Liouville - von Neumann equation for a time-dependent anharmonic oscillator. We find a variationally determined Gaussian approximation, as well as the number and the coherent states. The procedure is further developed to find systematically the perturbative corrections to the variational Gaussian approximation. By applying the method to a time-independent anharmonic oscillator, we show that the results agree with those of other variational perturbation theories, and we find that the system has an interesting algebraic structure at the first-order correction level.