A new method to derive low-lying N-dimensional quantum wave functions by quadratures along a single trajectory

摘要

We present a new method to derive low lying N-dimensional quantum wave functions by quadrature along a single trajectory. The N-dimensional Schroedinger equation is cast into a series of readily integrable first-order ordinary differential equations. Our approach resembles the familiar W.K.B. approximation in one dimension, but is designed to explore the classically forbidden region and has a much wider applicability than W.K.B. The current method also provides a perturbation series expansion and the Green functions of the wave equation in the N-dimension, all by quadratures along a single trajectory. A number of examples are given for illustration, including a simple algorithm to evaluate the Stark effect in closed form to any finite order of the electric field. (C) 2001 Academic Press. [References: 17]