Variational time-dependent perturbation scheme based on the hydrodynamic analogy to Schrödinger's equation

Abstract

A variational principle correct through the second order is presented for time‐dependent perturbations about a bound state. The formulation is based on the hydrodynamic analogy to quantum mechanics and is obtained by linearization of a general principle within the spirit of the acoustic approximation in classical fluid mechanics. The method requires the knowledge of the wavefunction for the unperturbed state only, unlike in the standard procedure of expansion in terms of a complete set of unperturbed wavefunctions. In dealing with the changes in the amplitude and phase of the wavefunction which are nonoscillatory, the method is expected to offer advantages over the usual variational perturbation methods which utilize the oscillatory wavefunctions directly. The method is applied to the calculation of the dynamic polarizability of the hydrogen atom and reasonable accuracy is obtained for an overly simple choice of basis functions.