On solutions of the Schrodinger equation for some molecular potentials: wave function ansatz

Download

index.pdf

Date

2008-09-01

Author

IKHDAİR, SAMEER
Sever, Ramazan

Metadata

Show full item record

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

Item Usage Stats

42
views

0
downloads

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 eigensolutions recover their standard analytical forms in literature.

Subject Keywords

optical character recognition, Diatomic molecules, Schrodinger equation, Anharmonic oscillator potential, Mie-type potential, Kratzer's potential, Pseudoharmonic potential, Bound states

URI

https://hdl.handle.net/11511/62579

Journal

CENTRAL EUROPEAN JOURNAL OF PHYSICS

DOI

https://doi.org/10.2478/s11534-008-0060-y

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

Exact solutions of the radial Schrodinger equation for some physical potentials IKHDAİR, SAMEER; Sever, Ramazan (2007-12-01) By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrodinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained. (C) Versita Warsaw and Springer-Verlag Berlin Heidelberg. 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.
Approximate analytical solutions of a two-term diatomic molecular potential with centrifugal barrier Arda, Altug; Sever, Ramazan (2012-08-01) Approximate analytical bound state solutions of the radial Schrodinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where q >= 1 and q = 0. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulthen potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.
Novel quantum description of time-dependent molecular interactions obeying a generalized non-central potential Menouar, Salah; Choi, Jeong Ryeol; Sever, Ramazan (2018-04-01) Quantum features of time-dependent molecular interactions are investigated by introducing a time-varying Hamiltonian that involves a generalized non-central potential. According to the Lewis-Riesenfeld theory, quantum states (wave functions) of such dynamical systems are represented in terms of the eigenstates of the invariant operator. Hence, we have derived the eigenstates of the invariant operator of the system using elegant mathematical manipulations known as the unitary transformation method and the Ni...
Analytical solutions of Schrodinger equation for the diatomic molecular potentials with any angular momentum Akçay, Hüseyin; Sever, Ramazan (2012-08-01) Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also considered. Algebraic method is used in the calculations.

Citation Formats

S. IKHDAİR and R. Sever, “On solutions of the Schrodinger equation for some molecular potentials: wave function ansatz,” CENTRAL EUROPEAN JOURNAL OF PHYSICS, pp. 697–703, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62579.