Modified Laguerre basis for hydrogen-like systems

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.


Improved analytical approximation to arbitrary l-state solutions of the Schrodinger equation for the hyperbolical potential
IKHDAİR, SAMEER; Sever, Ramazan (2009-04-01)
A new approximation scheme to the centrifugal term is proposed to obtain the l not equal 0 bound-state solutions of the Schrodinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding normalized wave functions are also found in terms of the Jacobi polynomials. To show the accuracy of the new proposed approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers n and l with two different values of the potential par...
On solutions of the Schrodinger equation for some molecular potentials: wave function ansatz
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...
Polynomial solutions of the Mie-type potential in the D-dimensional Schrodinger equation
IKHDAİR, SAMEER; Sever, Ramazan (2008-04-30)
The polynomial solution of the D-dimensional Schrodinger equation for a special case of Mie potential is obtained with an arbitrary l not equal 0 states. The exact bound state energies and their corresponding wave functions are calculated. The bound state (real) and positive (imaginary) cases are also investigated. In addition, we have simply obtained the results from the solution of the Coulomb potential by an appropriate transformation.
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.
Exact polynomial eigensolutions of the Schrodinger equation for the pseudoharmonic potential
Ikhdair, Sameer; Sever, Ramazan (2007-03-31)
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum l. The exact bound-state energy eigenvalues and the corresponding eigenfunctions are analytically calculated. The energy states for several diatomic molecular systems are calculated numerically for various principal and angular quantum numbers. By a proper transformation, this problem is also solved very simply by using the known eigensolutions of anharmonic oscillator potential.
Citation Formats
H. Taşeli, “Modified Laguerre basis for hydrogen-like systems,” INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, pp. 949–959, 1997, Accessed: 00, 2020. [Online]. Available: