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Journal of Dezhou University

非球谐振子势V(r)=Ar~2+Br~4+Cr~6 schrodinger方程的解析解

周国中, 何宝钢

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

根据波函数的有限性和非球谐振子势的渐近性质,通过待定非球谐振子势波函数的设定,得到势函数表示为V(r)=Ar2+Br4+Cr6的schrodinger方程的精确的能量本征值和本征波函数.通过对势参数制约关系、能量本征值和本征波函数的分析,得到相同势参数制约关系下多组能量本征值和本征波函数.

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根据波函数的有限性和非球谐振子势的渐近性质,通过待定非球谐振子势波函数的设定,得到势函数表示为V(r)=Ar2+Br4+Cr6的schrodinger方程的精确的能量本征值和本征波函数.通过对势参数制约关系、能量本征值和本征波函数的分析,得到相同势参数制约关系下多组能量本征值和本征波函数.
The solution of the Schrodinger equation with the physical potential is important part in quantum mechanics. The anharmonic potential is one of the physical potential that is interesting to be explored. Many methods have been developed to solve the Schrodinger equation. The Ansatz wave function method is one of the many methods that used to solve the Schrodinger equation. The Ansatz wave function method was used to solve the radial part of Schrodinger Equation. In this study we present the solution of the radial part Schrodinger equation in D-dimensional system with potential V(r)=ar2+br+cr-1+dr-2+er-3+fr-4. The important part in Ansatz wave function method is to determine the wave function Ansatz corresponding to the shape of the anharmonic potential that used. The Ansatz wave function determined by using supersymmetric approximation. By substituting the wave function Ansatz into Schrodinger equation and using algebraic we obtain the radial eigenfunction and the energy, and then the eigenfunction visualized.