A charged spinless particle in scalar-vector harmonic oscillators with uniform magnetic and Aharonov-Bohm flux fields

Abstract

The two-dimensional solution of the spinless Klein-Gordon (KG) equation for scalarvector 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 (x L = 0) and AB flux field (n = 0) case. Effects of external fields on the non-relativistic energy eigenvalues and wave functions solutions are also precisely presented.

Relativistic Bound States of Spinless Particle by the Cornell Potential Model in External Fields

“…The relativistic bound state solutions can also be obtained in this work for any mixture with ( ) = ( ), where | | ≤ 1. The significance of this bound on | | is the existence of energy eigenvalues (see [60][61][62][63][64] and references therein). The choice of the case = 1 is simply to reduce our solution to the nonrelativistic (Schrodinger) energy states of the single particle.…”

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], the superposition of pseudo-harmonic, linear and Columbic potential forms [62], the Coulomb plus linear [63], the anharmonic oscillator [64], the Hulthen [65], the Coulomb-like [66] and the Killingbeck potentials [67] in the presence of the external magnetic and AB flux fields.…”

Thermodynamic properties and approximate solutions of the ℓ-state Pöschl–Teller-type potential

“…The results obtained by solving wave equations for certain potential models are increasingly being applied. Recently, the solution of the two-dimensional spinless Klein-Gordon equation for scalar-vector harmonic oscillator potentials with and without the constant perpendicular magnetic and Aharonov-Bohm (AB) flux fields was studied by Ikhdair and Falaye (2014). The energies and wave functions of certain potential models have also been used to obtain information-theoretic measures such as Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy among other information-theoretic measures (see e.g Yahya et al, 2014b).…”