Relativistic Two-Dimensional Harmonic Oscillator Plus Cornell Potentials in External Magnetic and AB Fields

Sameer M Ikhdair,Ramazan Sever

doi:10.1155/2013/562959

Abstract

The Klein-Gordon (KG) equation for the two-dimensional scalar-vector harmonic oscillator plus Cornell potentials in the presence of external magnetic and Aharonov-Bohm (AB) flux fields is solved using the wave function ansatz method. The exact energy eigenvalues and the wave functions are obtained in terms of potential parameters, magnetic field strength, AB flux field, and magnetic quantum number. The results obtained by using different Larmor frequencies are compared with the results in the absence of both magnetic field (ωL= 0) and AB flux field (ξ=0) cases. Effect of external fields on the nonrelativistic energy eigenvalues and wave function solutions is also precisely presented. Some special cases like harmonic oscillator and Coulombic fields are also studied.

Highlights

The exact solution of Schrodinger equation (SE) and the relativistic wave equations for some physical potentials are very important in many fields of physics and chemistry since they contain all the necessary information for the quantum system under investigation
In this paper, we have studied the solution of two-dimensional KG and Schrodinger equations with the Killingbeck potential for low vibrational and rotational energy levels without and with a constant magnetic field having arbitrary Larmor frequeny and AB flux field
We have applied the wave function ansatz method for ωL ≠ 0 and ξ ≠ 0 to obtain analytical expressions, in closed form, for bound state energies and wave functions of the spinless relativistic particle subject to a Killingbeck interaction expressed in terms of external uniform magnetic and AB flux fields in any vibrational n and rotational m states

Summary

Introduction

The exact solution of Schrodinger equation (SE) and the relativistic wave equations for some physical potentials are very important in many fields of physics and chemistry since they contain all the necessary information for the quantum system under investigation. The Schrodinger equation is solved exactly for its bound states (energy spectrum and wave functions) [27,28,29] to study the spectral properties in a 2D charged particle (electron or hole) confined by a harmonic oscillator in the presence of external strong uniform magnetic field →󳨀B along the z direction and Aharonov-Bohm (AB) flux field created by a solenoid. We studied the scalar charged particle exposed to relativistic scalar-vector Killingbeck potentials in presence of magnetic and Aharonov-Bohm flux fields and obtained its energy eigenvalues and wave functions using the analytical exact iteration method [39].

The Klein-Gordon Atom

Discussions

Concluding Remarks