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arXiv:1205.4141 · Chinese Physics B

Effects of external fields on a two-dimensional Klein—Gordon particle under pseudo-harmonic oscillator interaction

Sameer M. Ikhdair, Majid Hamzavi

Published Nov 1, 2012• 38 citations
arXivHTMLPDF

Abstract

We study the effects of the perpendicular magnetic and Aharonov—Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein—Gordon (KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator (PHO). We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov—Uvarov (NU) method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.

DOI
10.1088/1674-1056/21/11/110302

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We study the effects of the perpendicular magnetic and Aharonov—Bohm (AB) flux fields on the energy levels of a two-dimensional (2D) Klein—Gordon (KG) particle subjected to an equal scalar and vector pseudo-harmonic oscillator (PHO). We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential parameter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov—Uvarov (NU) method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.
The two-dimensional solution of the spinless Klein–Gordon (KG) equation for scalar–vector harmonic oscillator potentials with and without the presence of constant perpendicular magnetic and Aharonov–Bohm (AB) flux fields is studied within the asymptotic function analysis and Nikiforov–Uvarov (NU) method. The exact energy eigenvalues and normalized wave functions are analytically 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) case. Effects of external fields on the non-relativistic energy eigenvalues and wave functions solutions are also precisely presented.
In this work, we examine the thermo-magnetic characteristics and energy spectra of a system exposed to both magnetic and Aharonov–Bohm (AB) fields with the existence of an interaction potential that is pseudo-harmonic. Explicit calculations of the eigen-solutions are performed with the expanded Nikiforov–Uvarov formalism. The confluent Heun function is used to represent the equivalent wave functions. If the AB and magnetic fields are gone, quasi-degeneracy in the system’s energy levels is shown by a numerical analysis of the energy spectrum. Additionally, we provided a visual representation of how the AB and magnetic fields affected the system’s thermo-magnetic characteristics. Our results show a strong dependence of thermo-magnetic properties on temperature, screening parameters, external magnetic fields, and AB fields.
In this work, the non-relativistic wave equation via the Schrödinger wave equation under the influence of the Aharonov-Bohm flux field Subject to physical potentials of various kinds is investigated. These potentials are modified Coulomb potential, modified harmonic oscillator potential, the Kratzer-Feus potential, and the Mie-type potential which have wide applications in different branches of physics and chemistry. We solve the Schrodinger wave equation using the Nikiforov-Uvarov (NU) method and obtain the energy profiles and the wave function of the non-relativistic particle, and analyze the effects of potential and the quantum flux on them. We show that each non-relativistic energy level gets modified in comparison to the known results obtained in the literature.
The Killingbeck potential consists of oscillator potential plus Cornell potential, i.e. ar2+ br - c/r, that it has received a great deal of attention in particle physics. In this paper, we study the energy levels and wave function for arbitrary m-state in two-dimensional (2D) Schrödinger equation (SE) with a Killingbeck potential under the influence of strong external uniform magnetic and Aharonov–Bohm (AB) flux fields perpendicular to the plane where the interacting particles are confined. We use the wave function ansatz method to solve the radial problem of the Schrödinger equation with Killingbeck potential. We obtain the energy levels in the absence of external fields and also find the energy levels of the familiar Coulomb and harmonic oscillator potentials.
We investigate the thermo-magnetic properties of the Attractive Radial Potential (ARP) for a particle moving in two-dimensional non-relativistic Schrödinger equation subjected to an external magnetic field and Aharonov-Bohm (AB) flux. Analytical solution for the energy eigenvalues and wavefunctions were obtained in a closed form via the Nikiforov-Uvarov Functional Analysis (NUFA) method. We derived the partition function by analyzing the system as a canonical ensemble to obtain the expressions for the thermodynamic quantities which include the free energy, entropy, specific heat capacity and internal energy. Our results show a decrease in the energy spectrum when the AB flux and magnetic fields are increased. At low temperatures, specific heat capacity shows a peak anomaly, while Helmholtz free energy and entropy exhibit temperature dependence. We also observed that AB flux and magnetic field influence both magnetization and magnetic susceptibility and exhibit both paramagnetic and diamagnetic behavior. The findings provide valuable insights into in molecular physics applications.
In this article, the Varshni potential is analyzed taking into consideration the effects of magnetic and AB flux fields within the non-relativistic regime using the Nikiforov-Uvarov-Functional Analysis method (NUFA) method. The energy equation and wave function of the system are obtained in close form. We find that the entirety of effects of these fields removes degeneracy as a consequence and raises the bound state energy of the system. More so, it could be deduced that to regulate the energy spectra of this system, the AB-flux and magnetic field will do so greatly. The results from this study can be applied in condensed matter physics, atomic and molecular physics.