A New Method to Derive Low-Lying N-dimensional Quantum Wave Functions by Quadratures Along a Single Trajectory
Abstract
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 method also provides a perturbation series expansion and the Green's functions of the wave equation in 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.
Cite
@article{arxiv.quant-ph/0005039,
title = {A New Method to Derive Low-Lying N-dimensional Quantum Wave Functions by Quadratures Along a Single Trajectory},
author = {R. Friedberg and T. D. Lee and W. Q. Zhao},
journal= {arXiv preprint arXiv:quant-ph/0005039},
year = {2009}
}
Comments
69 pages, Latex, no figure, no table; more ackowledgment added, typos corrected