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

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.

Superstatistics of Schrödinger equation with pseudo-harmonic potential in external magnetic and Aharanov-Bohm fields

“…The solutions of the Schrödinger equation in a 2D charged particles confined by a harmonic oscillator in the presence of external magnetic field along the z-axis and Aharonov Bohm(AB) flux field created by solenoid have been studied by many authors [24][25][26][27]. Also, other effects of external magnetic fields on different physical systems have been investigated [28]. Koscik and Okopinska investigated the quasi exact solutions for two interacting electrons using Coulombic force with confined anisotropic harmonic oscillator in 2D anisotropic dot [29].…”

Relativistic Killingbeck energy states under external magnetic fields

“…Also, in recent years, the exact analytical solutions of the Dirac equation have been extensively obtained, by using various methods in the presence of the spin and p-spin symmetries (see, for example, [48][49][50][51][52][53][54][55][56][57][58]). On the other hand, some authors have studied both the non-relativistic and relativistic bound states with some potential models such as Cornell [59], harmonic oscillator [60], sum of harmonic oscillator and Cornell [61],…”

Analytical Solutions of the Schrödinger Equation with Kratzer-screened Coulomb Potential for a Quarkonium System

“…The screened Coulomb potential is a short-range potential [38]. In solid-state physics, it describes the charge particle effects of conduction electrons [39]. It takes the form…”