幂函数叠加势的径向薛定谔方程的解析解  

The analytic solution of the radial Schrdinger equation for the superposed potentials

作　　者：胡先权[1] 罗光[1] 马燕[1] 崔立鹏[1] 

机构地区：[1]重庆师范大学物理学与信息技术学院,重庆400047

出　　处：《物理学报》2009年第4期2168-2173,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:10575140);重庆市教育委员会基础理论研究基金(批准号:KJ080825)资助的课题~~

摘　　要：研究多种正幂势函数与逆幂势函数紧密耦合条件下薛定谔径向方程解析解的求解方法.对势函数为V(r)=α1r8+α2r3+α3r2+β3r-1+β2r-3+β1r-4的径向薛定谔方程存在解析解的条件以及精确的解析解进行了研究.根据量子系统波函数必须满足单值、有界和连续的标准条件,首先求出径向坐标r→∞以及r→0时的渐近解,然后采用非正则奇点邻域附近的波函数级数解法与求得的渐近解相结合,通过幂级数系数比较法得到径向薛定谔方程在势函数系数紧密耦合条件下的一系列定态波函数解析解以及相应的能级结构,并作适当讨论与结论.The method of solving the radial Schrdinger equation is studied by under the tight coupling condition of several positive-power and inverse-power potential functions.The precise analytic solutions and the conditions that determine the existence of analytic solution are searched when the potential of the radial Schrdinger equation is V（r）=α1r^8＋α2r^3＋α3r^2＋β3r^-1＋β2r^-3＋β1r^-4.According to the single valued,bounded and continuous stipulations of wave function in a quantum system,firstly,the asymptotic solution is solved when the radial coordinate r→∞ and r→0;secondly,the asymptotic solutions are combined with the series solutions in the neighborhood of irregular singularities;and then the power series coefficients are compared.A series of analytic solutions of the stationary state wave function and the corresponding energy level structure are deduced by tight coupling between the coefficients of potential functions for the radial Schrdinger equation.And the solutions are discussed and the conclusions are made.

关 键 词：级数解法 幂势函数 径向波函数 渐近解 

分 类 号：O411[理学—理论物理]