非球谐环形振子势的Schrdinger方程的解析解  

Analytic Solution of the Schrdinger Equation in the Non-spherical Ring Shaped Oscillator

作　　者：王帮美[1] 胡先权[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：《重庆师范大学学报（自然科学版）》2008年第2期62-66,共5页Journal of Chongqing Normal University:Natural Science

基　　金：重庆市教委基础理论研究基金(No.KJ060812)

摘　　要：量子力学中除了无限深势阱、一维线性谐振子、库仑势和三维各向同性谐振子势外,绝大部分Schrdinger方程是没有精确解的,这给具体问题的深入研究带来了很大的障碍。本文从求解Schrdinger方程的NU Method方法出发,求解了非球谐环形振子势V(r,θ)=μω2r2/2+h-2α/(2μr2)+-h2βcosθ/(2μr2sin2θ)的本征方程的角向方程,获得解析解,将求解的过程大大简化;同时用特殊函数的方法求解了非球谐环形振子势的Schrdinger方程的径向方程,借以拓宽对Schrdinger方程求解方法的研究。Most of Schrodinger equations in quantum mechanics haven＇ t analytic solutions except the problems of well with infinite depth, one-dimensional linear harmonic oscillator and Coulomb＇ s potential as well as three-dimensional isotropic harmonic oscillator. These Schrodinger equations include the various equations in the non-spherical ring shaped oscillator potential that haven＇t analytic solutions. We can only solve these problems approximately in our research activities, but the solving process of these problems is often exceptional complex. The limitation handicaps us to lucubrate the idiographic problems. This paper adopts NU Method（A. F, Nikiforov- V. B. Uvarov Method） to solve the angular equation of the Schrodinger equation in the non-spherical ring shaped oscillator potential V（r,θ）=μω^2r^2/2＋h^2α/（2μr^2）＋h^2βcosθ/（2μr^2sinθ） We decompose the Schrodinger equation in the non-spherical ring shaped oscillator potential step by step until we obtains the analytic solutions of the equation, thus we obtain the analytic solution of the angular eigenfunction, and simplify the process of solutions. Moreover, this paper adopts special functions in the radial equation at the same time to broaden our study in solving the Schrodinger equations.

关 键 词：非球谐环形振子势 SCHRODINGER方程 角向方程 径向方程 

分 类 号：O441.1[理学—电磁学]