Bessel basis with applications: N-dimensional isotropic polynomial oscillators

Date

1997-06-20

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

176
views

0
downloads

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 general anharmonic oscillators and the confinement potentials of the farm V(r) = -Z/r + Sigma(i=1)(K-1) c(i)r(i) is also discussed. (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/11511/38980

Journal

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY

DOI

https://doi.org/10.1002/(sici)1097-461x(1997)63:5<935::aid-qua4>3.0.co;2-x

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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.
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...
A Fourier-Bessel expansion for solving radial Schrodinger equation in two dimensions Taşeli, Hasan (Wiley, 1997-02-15) 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 ...
Covariant Bethe-Salpeter equation for heavy Q(Q)over-bar bound states Zakout, I; Sever, Ramazan (IOP Publishing, 1997-02-01) We investigate a numerical solution of the covariant Bethe-Salpeter equation in the Euclidean space for heavy meson with gluon ladder in the Landau gauge and scalar confinement. A new approach is presented to solve the non-linear eigenvalue problem with suitable bases and fictitious eigenvalue parameters. We obtain unphysical states when the equation is solved for timelike spectra. We also present how to cover the singularity of a free quark propagator and Schwinger-Dyson equation when extrapolated to the ...
Algebraic approaches to eigenvalue equations: The Wronskian method Yurtsever, Ersin (Elsevier BV, 1987-11) A recently proposed method for the solution of eigenvalue equations is applied to two different model potentials. Considerable improvements are observed if the algebraic requirements of the Wronskian method are enforced over a region instead of at a single point.

Citation Formats

H. Taşeli, “Bessel basis with applications: N-dimensional isotropic polynomial oscillators,” INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, pp. 935–947, 1997, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38980.