Relativistic Killingbeck energy states under external magnetic fields

Abstract

We address the behavior of the Dirac equation with the Killingbeck radial potential including the external magnetic and Aharonov-Bohm (AB) flux fields. The spin and pseudo-spin symmetries are considered. The correct bound state spectra and their corresponding wave functions are obtained. We seek such a solution using the biconfluent Heun's differential equation method. Further, we give some of our results at the end of this study. Our final results can be reduced to their non-relativistic forms by simply using some appropriate transformations. The spectra, in the spin and pseudo-spin symmetries, are very similar with a slight difference in energy spacing between different states.

Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

“…Recently, a * Email corresponding author: eshgi54@gmail.com; m.eshghi@semnan.ac.ir considerable interest, in the mass dependence on the inter-nuclear distance, has been revived in solving different equations with various physical potential models [18][19][20][21][22][23][24][25][26][27][28][29]. Furthermore, a number of works takes the effect of an electric or magnetic fields into account in studying different systems [30][31][32][33][34]. For further study we cite Refs.…”

Effects of Topological Defect on the Energy Spectra and Thermo-magnetic Properties of $$CO$$ Diatomic Molecule

“…Given the energy spectrum (37), the partition function   Z  of the screened modified Kratzer potential at finite temperature T is obtained with the Boltzmann factor as [50];…”

“…The Dirac-Weyl equation was solved with the Nikoforov-Uvarov (NU) and Frobenius methods. Thermal properties was obtained using the Hurwitz zeta function method for one of the states [33] and other numerous studies [34][35][36][37][38][39][40].…”

Schrödinger equation based analytic assessment of thermal properties of confined electrons under vector and scalar fields

“…[37][38][39] However, a large number of potentials of physical importance used into the Schrödinger equation or the perturbations into Dirac and Dirac-Weyl equations may be transformed into the form of the biconfluent Heun function (BHF). [40][41][42][43][44][45][46][47][48] Moreover, from a century ago, the Schrödinger equation can be reduced to the BHF known in mathematics for harmonium. 49,50 Although, some of the authors have submitted different solvable traditional models as analytically, [51][52][53][54][55] and there are a few works about of the geometric model in these areas.…”

“…[56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74] Also, a number of works take the effects of an electric or magnetic fields into account in studying different systems. [41][42][43][44]75,76 In this regard, Yuce has solved the Schrödinger equation analytically for a charged particle interacting with the plane-wave electromagnetic field. 6 Unal et al have investigated electric field effects the refractive index changes in a modified Poschl-Teller quantum well.…”