沿一条确定的轨迹积分求解N维基态量子波函数的新方法  

A NEW METHOD TO DERIVE LOW-LYING N-DIMENSIONAL QUANTUMWAVE FUNCTIONS BY QUADRATURES ALONG A SINGLE TRAJECTORY

作　　者：R.弗里德伯格 李政道[1] 赵维勤[1] 

机构地区：[1]哥伦比亚大学物理系,美国纽约ny10027

出　　处：《物理》2001年第5期294-299,共6页Physics

摘　　要：介绍了一个沿着一条确定的轨迹积分求解N维基态量子波函数的新方法 .通过对哈密顿量的位势引入标度因子g2 ,将波函数和能量按 1 g展开 ,并应用求解经典的Hamilton -Jacobi方程的方法 ,找到一条确定的轨迹 ,使薛定谔方程从二阶偏微分方程化为一系列沿这条轨迹的一阶常微分方程 .基态波函数可以表示为沿这条确定轨迹的一系列积分 ,而能量则可以用位势极小值处的一系列微分表示 .在此基础上 ,导得一个全新的微扰展开系列和相应的N维量子波函数的格林函数 .作为例子 ,将此方法应用于库仑吸引位和斯塔克 (Stark)效应 .A new method to solve N dimensional ground state quantum wave functions is developed based on quadratures along a single trajectory. By introducing a scaling factor g+2 in the potential, expanding the wave function and energy in terms of 1/ g, and employing the method of solving the classical Hamilton-Jacobi equation, the second order partial differential Schrdinger equation is cast into a series of first order ordinary differential equations. The ground state wave function can be expressed as a series of integrations along the trajectory and the energy as a series of differentials at the minimum of the potential.A new perturbation expansion is obtained based on this method. The corresponding N -dimensional Green function is derived. As an example,this method is applied to an attractive Coulomb potential and the Stark effect.

关 键 词：轨迹积分子 格林函数 N维基态量子波函数 微扰展开系列 标度因子 库仑吸引位 斯塔克效应 

分 类 号：O413.1[理学—理论物理]