Novel quantum description of time-dependent molecular interactions obeying a generalized non-central potential

Date

2018-04-01

Author

Menouar, Salah
Choi, Jeong Ryeol
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

181
views

0
downloads

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 Nikiforov-Uvarov method. Based on full wave functions that are evaluated by considering such eigenstates, quantum properties of the system are analyzed. The time behavior of probability densities which are the absolute square of the wave functions are illustrated in detail. This research provides a novel method for investigating quantum characteristics of complicated molecular interactions. The merit of this research compared to conventional ones in this field is that time-varying parameters, necessary for the actual description of intricate atomic and molecular behaviors with high accuracy, are explicitly considered.

Subject Keywords

Time-dependent systems, Non-central potential, Modified Kratzer potential, Unitary transformation, Schrodinger equation

URI

https://hdl.handle.net/11511/62765

Journal

NONLINEAR DYNAMICS

DOI

https://doi.org/10.1007/s11071-018-4081-9

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

Combining perturbation theory and transformation electromagnetics for finite element solution of Helmholtz-type scattering problems Kuzuoğlu, Mustafa (2014-10-01) A numerical method is proposed for efficient solution of scattering from objects with weakly perturbed surfaces by combining the perturbation theory, transformation electro-magnetics and the finite element method. A transformation medium layer is designed over the smooth surface, and the material parameters of the medium are determined by means of a coordinate transformation that maps the smooth surface to the perturbed surface. The perturbed fields within the domain are computed by employing the material p...
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.
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...
Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum Akçay, Hüseyin; Sever, Ramazan (2013-11-01) Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Poschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.
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. Menouar, J. R. Choi, and R. Sever, “Novel quantum description of time-dependent molecular interactions obeying a generalized non-central potential,” NONLINEAR DYNAMICS, pp. 659–671, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62765.