一种沿单轨迹求积求低态N维量子波函数的新方法
A New Method to Derive Low-Lying N-dimensional Quantum Wave Functions by Quadratures Along a Single Trajectory
摘要：
本文提出了一种新的方法，通过沿一条轨迹求积，导出了N维量子波函数。将N维薛定谔方程转化为一系列易积的一阶常微分方程。我们的方法类似于熟悉的WKB。在一维近似，但旨在探索经典的禁戒区，并具有更广泛的适用性比W.K.B.。该方法还提供了一个扰动级数展开和格林函数的波动方程在N维，所有的求积沿一个单一的轨迹。给出了一些例子进行说明，包括一个简单的算法来评估斯塔克效应的封闭形式的任何有限阶的电场。
英文摘要：
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 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
