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

We have developed a variational perturbation theory based on the Liouville- von Neumann equation for a time-dependent anharmonic oscillator. We End a v ariationally determined Gaussian approximation, as well as the number and t he coherent states. The procedure is further developed to find systematical ly 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 theori es, and we find that the system has an interesting algebraic structure at t he first-order correction level.