Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
A Fourier-Bessel expansion for solving radial Schrodinger equation in two dimensions
Date
1997-02-15
Author
Taşeli, Hasan
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
211
views
0
downloads
Cite This
The spectrum of the two-dimensional Schrodinger equation for polynomial oscillators bounded by infinitely high potentials, where the eigenvalue problem is defined on a finite interval r is an element of [0, L), is variationally studied. The wave function is expanded into a Fourier-Bessel series, and matrix elements in terms of integrals involving Bessel functions are evaluated analytically. Numerical results presented accurate to 30 digits show that, by the time L approaches a critical value, the tow-lying state energies behave almost as if the potentials were unbounded. The method is applicable to multiwell oscillators as well. (C) 1997 John Wiley & Sons, Inc.
Subject Keywords
Physical and Theoretical Chemistry
,
Atomic and Molecular Physics, and Optics
,
Condensed Matter Physics
URI
https://hdl.handle.net/11511/38382
Journal
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
DOI
https://doi.org/10.1002/(sici)1097-461x(1997)61:5<759::aid-qua3>3.0.co;2-v
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
ACCURATE COMPUTATION OF THE ENERGY-SPECTRUM FOR POTENTIALS WITH MULTIMINIMA
Taşeli, Hasan (Wiley, 1993-01-01)
The eigenvalues of the Schrodinger equation with a polynomial potential are calculated accurately by means of the Rayleigh-Ritz variational method and a basis set of functions satisfying Dirichlet boundary conditions. The method is applied to the well potentials having one, two, and three minima. It is shown, in the entire range of coupling constants, that the basis set of trigonometric functions has the capability of yielding the energy spectra of unbounded problems without any loss of convergence providin...
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.
The Dirac-Yukawa problem in view of pseudospin symmetry
AYDOĞDU, OKTAY; Sever, Ramazan (IOP Publishing, 2011-08-01)
An approximate analytical solution of the Dirac equation for the Yukawa potential under the pseudospin symmetry condition is obtained using the asymptotic iteration method. We discover the energy eigenvalue equation and some of the numerical results are listed. Wave functions are obtained in terms of hypergeometric functions. Extra degeneracies are removed by adding a new term, A/r(2), to the Yukawa potential. The effects of tensor interaction on the two states in the pseudospin doublet are also investigated.
Bessel basis with applications: N-dimensional isotropic polynomial oscillators
Taşeli, Hasan (Wiley, 1997-06-20)
The efficient technique of expanding the wave function into a Fourier-Bessel series to solve the radial Schrodinger equation with polynomial potentials, V(r) = Sigma(i=1)(K) v(2i)r(2i), in two dimensions is extended to N-dimensional space. It is shown that the spectra of two- and three-dimensional oscillators cover the spectra of the corresponding N-dimensional problems for all N. Extremely accurate numerical results are presented for illustrative purposes. The connection between the eigenvalues of the gene...
A perturbative treatment for the bound states of the Hellmann potential
Ikhdair, Sameer M.; Sever, Ramazan (Elsevier BV, 2007-05-14)
A new approximation formalism is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential -a/r and the Yukawa potential bexp(-delta r)/r of arbitrary strength h and screening parameter delta. Although the analytic expressions for the energy eigenvalues E(n,l) yield quite accurate results for a wide range of n, f in the limit of very weak screening, the results become gradually worse as the strength b and the screening coefficient 6 i...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
H. Taşeli, “A Fourier-Bessel expansion for solving radial Schrodinger equation in two dimensions,”
INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY
, pp. 759–768, 1997, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38382.