A variational perturbation theory

Abstract

The paper discusses how the variationally improved perturbation theory VIPT scheme of approximation in quantum mechanics can be improved convergence-wise if one uses for variational trial functions the perturbative series with variational parameter, so that one is effectively doing variational calculations directly on the high order perturbative series for energy. The result optimizes the high order energy directly and thus represents a significant improvement over the VIPT procedure. When applied to a double potential in which even the VIPT is badly divergent, we saw that the result is still very much convergent.