The Laguerre pseudospectral method for the radial Schrodinger equation

Taşeli, Hasan
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 eigenfunction expansion for the Schrodinger equation with arbitrary non-central potentials
Taşeli, Hasan; Uğur, Ömür (2002-11-01)
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...
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IKHDAİR, SAMEER; Sever, Ramazan (2008-09-01)
Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrodinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, delta and nu are also given, where eta depends on a linear combination of the angular momentum quantum number l and the spatial dimensions D and delta is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigenso...
Modified Laguerre basis for hydrogen-like systems
Taşeli, Hasan (1997-06-20)
N-dimensional Schrodinger equation with isotropic nonpolynomial perturbations is studied. A Laguerre basis, which is different from that of the hydrogen atom in nature, has been introduced and applied to screened Coulomb potentials. Certain very useful recurrence relations are developed for the evaluation of matrix elements analytically. Specimen eigenvalue calculations to illustrate the method as well as its extension to other potentials are presented. (C) 1997 John Wiley & Sons, Inc.
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...
The finite element method over a simple stabilizing grid applied to fluid flow problems
Aydın, Selçuk Han; Tezer-Sezgin, Münevver; Department of Scientific Computing (2008)
We consider the stabilized finite element method for solving the incompressible Navier-Stokes equations and the magnetohydrodynamic (MHD) equations in two dimensions. The well-known instabilities arising from the application of standard Galerkin finite element method are eliminated by using the stabilizing subgrid method (SSM), the streamline upwind Petrov-Galerkin (SUPG) method, and the two-level finite element method (TLFEM). The domain is discretized into a set of regular triangular elements. In SSM, the...
Citation Formats
H. ALICI and H. Taşeli, “The Laguerre pseudospectral method for the radial Schrodinger equation,” APPLIED NUMERICAL MATHEMATICS, pp. 87–99, 2015, Accessed: 00, 2020. [Online]. Available: