An eigenfunction expansion for the Schrodinger equation with arbitrary non-central potentials

Date

2002-11-01

Author

Taşeli, Hasan
Uğur, Ömür

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

259
views

0
downloads

An eigenfunction expansion for the Schrodinger equation for a particle moving in an arbitrary non-central potential in the cylindrical polar coordinates is introduced, which reduces the partial differential equation to a system of coupled differential equations in the radial variable r. It is proved that such an orthogonal expansion of the wavefunction into the complete set of Chebyshev polynomials is uniformly convergent on any domain of (r, theta). As a benchmark application, the bound states calculations of the quartic oscillator show that both analytical and numerical implementations of the present method are quite satisfactory.

Subject Keywords

Two-dimensional Schrodinger equation, Eigenfunction expansion, Eigenvalue problems

URI

https://hdl.handle.net/11511/32558

Journal

JOURNAL OF MATHEMATICAL CHEMISTRY

DOI

https://doi.org/10.1023/a:1022949421571

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

The Sturm-Liouville operator on the space of functions with discontinuity conditions Uğur, Ömür (2006-03-01) The Sturm-Liouville differential operators defined on the space of discontinuous functions, where the moments of discontinuity of the functions are interior points of the interval and the discontinuity conditions are linear have been studied. Auxiliary results concerning the Green's formula, boundary value, and eigenvalue problems for impulsive differential equations are emphasized.
The Laguerre pseudospectral method for the radial Schrodinger equation ALICI, HAYDAR; Taşeli, Hasan (2015-01-01) By transforming dependent and independent variables, radial Schrodinger equation is converted into a form resembling the Laguerre differential equation. Therefore, energy eigenvalues and wavefunctions of M-dimensional radial Schrodinger equation with a wide range of isotropic potentials are obtained numerically by using Laguerre pseudospectral methods. Comparison with the results from literature shows that the method is highly competitive. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation Kaya, Ruşen; Taşeli, Hasan; Department of Mathematics (2019) In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those r...
An integral equation approach to the computation of nonlinear fields in electrical machines Kükrer, Osman; Ertan, H. Bülnet (Institute of Electrical and Electronics Engineers (IEEE), 1988-7) A numerical method based on an integral equation formulation, for the computation of nonlinear magnetostatic field, in two dimensions in cylindrical polar coordinates is given. The correctness of the method is illustrated by solving two linear two-dimensional magnetic field problems which have readily available analytical solutions. The dependence of the accuracy of the solution on the number and distribution of the meshes is studied on these examples. The method is then applied to the computation of the no...
An algebraic method for the analytical solutions of the Klein-Gordon equation for any angular momentum for some diatomic potentials Akçay, Hüseyin; Sever, Ramazan (IOP Publishing, 2014-01-01) Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second-order differential equation. Differential equations of this standard form are solvable in terms of hypergeometric functions and we give an algebraic formulation for the bound state wave functions and for the energy eigenvalues. This formulation is applied for the solutions of the Klein-Gordon equation with some diatomic potentials.

Citation Formats

H. Taşeli and Ö. Uğur, “An eigenfunction expansion for the Schrodinger equation with arbitrary non-central potentials,” JOURNAL OF MATHEMATICAL CHEMISTRY, pp. 323–338, 2002, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32558.