Journal of Anhui Normal University

ANALYTIC SOLUTION TO THE SCHRDINGER EQUATION FOR THE ANHARMONIC OSCILLATOR

Zhou Guo-zhong

Published Jan 1, 2005• 0 citations

Abstract

using an ansatz for the eigenfunction,we obtain the analytic solution to the Schrdinger equation for the anharmonic oscillator potential.In the bound states,the results show that parameters w′,d′,c′,b′ and a′ in the model potential have to satisfy relevant restraint conditions.

Related papers

ANALYTIC SOLUTION TO THE SCHRDINGER EQUATION WITH A HARMONIC OSCILLATOR POTENTIAL PLUS δ-POTENTIAL

Qinglin Peng

The analytic solution to the Schrodinger equation with a harmonic oscillator potentialplus δ-potential is presented in the coordinate representation. Its algebraic expression in theenergy representation is also given. The degeneracy of the energy levels is discussed and acomparison between the energy spectra of a harmonic oscillator and a particle in a δ-poten-tial is made.

Science China MathematicsJan 1, 19910 citations

THE EXACT SOLUTION OF ANHARMONIC OSCILLATOR POTENTIAL AND THE DESCRIPTION OF DOUBLE-WAVE FUNCTION

Chen Chang-Yuan, LIU YOU-WEN, 盐城师范专科学校物理系，盐城 224002

In this paper,the Schrdinger equation with an anharmonic oscillator potential V(x)=x2/2+g/2x2 is solved.The exact energy equation and the normalized wave function are obtained.The double-wave function quantum theory is applied to gain the time evolution equation to describe the physical quantities of a single motional particle in the anharmonic oscillator.

Acta Physica SinicaJan 1, 19981 citation

THE EXACT SOLUTION OF ANHARMONIC OSCILLATOR POTENTIAL AND THE DESCRIPTION OF DOUBLE WAVE FUNCTION

Yan-Feng Hang

Abstract In this paper,the Schrdinger equation with an anharmonic oscillator potential V(x)=x 2/2+ g/2x 2 is solved.The exact energy equation and the normalized wave function are obtained.The double wave function quantum theory is applied to gain the time evolution equation to describe the physical quantities of a single motional particle in the anharmonic oscillator.

Acta Physica SinicaJan 1, 19980 citations

Analytic solution to the schrdinger equation for the superposition potential V(r)=B_6■+B_5■+B_4■+B_3■+B_2■+B_1r

Zhou Guo-zhong

Using an ansatz for the eigenfunction,we obtain the analytic solution to the schrdinger equation for the superposition potential V(r)=B_6r~6+B_5r~5+B_4r~4+B_3r~3+B_2r~2+B_1r.

Journal of Guizhou Normal UniversityJan 1, 20060 citations

Bound state solutions of the one-dimensional Schrdinger equation for the harmonic oscillator via the Laplace transform

Zidong Chen

AbstrcatThe second-order one-dimensional Schrdinger differential equation for the harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform,and then,its solutions are obtained by means of directly making use of an integral.The energy spectrum is derived from the condition that the wave functions must be single-valued.The required eigenfunctions are obtained by applying the expansions of series and inverse Laplace transform.

College PhysicsJan 1, 20050 citations

Analytic Solution of the Schrdinger Equation in the Non-spherical Ring Shaped Oscillator

HU Xian-quan

Most of Schrdinger 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 Schrdinger 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 Schrdinger equation in the non-spherical ring shaped oscillator potential V(r,θ)=μω2r2/2+2α/(2μr2)+2βcosθ/(2μr2sin2θ).We decompose the Schrdinger 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 Schrdinger equations.

Chongqing Shifan Daxue xuebao. Ziran kexue banJan 1, 20080 citations