Relativistic Killingbeck Energy States Under an 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 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.

arXiv comment18 pages, 8 figures

References in corpus (33)

• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Pseudo-spin as a Relativistic Symmetry
• Dirac and Klein-Gordon equations with equal scalar and vector potentials
• Hidden pseudospin and spin symmetries and their origins in atomic nuclei
• The pseudo-spin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line
• Spin symmetry in the anti-nucleon spectrum
• On the Relativistic Foundations of Pseudospin Symmetry in Nuclei
• Generalized Pseudo-SU(3) Model and Pairing
• Relativistic Harmonic Oscillator with Spin Symmetry
• Test of Pseudospin Symmetry in Deformed Nuclei
• Graphene Dirac fermions in one-dimensional inhomogeneous field profiles: Transforming magnetic to electric field
• Nonrelativistic molecular models under external magnetic and AB flux fields
• An improved approximation scheme for the centrifugal term and the Hulthen potential
• Relativistic quantum mechanics with trapped ions
• Exact Klein-Gordon equation with spatially-dependent masses for unequal scalar-vector Coulomb-like potentials
• Pseudospin symmetry in single particle resonances in spherical square wells
• Perturbative interpretation of relativistic symmetries in nuclei
• Consequences of a Relativistic Pseudospin Symmetry for Radial Nodes and Intruder Levels in Nuclei
• Pseudospin symmetry in supersymmetric quantum mechanics: Schrödinger equations
• Spin and pseudospin symmetries in the antinucleon spectrum of nuclei
• Spin symmetry in Dirac negative energy spectrum in density-dependent relativistic Hartree-Fock theory
• Pseudospin symmetry in supersymmetric quantum mechanics: II. Spin-orbit effects
• On the effective Dirac dynamics of ultracold atoms in bichromatic optical lattices
• Optical lattice quantum simulator for QED in strong external fields: spontaneous pair creation and the Sauter-Schwinger effect
• On polynomial solutions of Heun equation
• Generalized Spin and Pseudo-Spin Symmetry: Relativistic Extension of Supersymmetric Quantum Mechanics
• Klein-Gordon and Dirac Equations with Thermodynamic Quantities
• Dirac bound states of anharmonic oscillator in external fields
• Beyond the constant-mass Dirac physics: Solitons, charge fractionization, and the emergence of topological insulators in graphene rings
• General spin and pseudospin symmetries of the Dirac equation
• Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential

Cited by in corpus (5)

• Energy spectra and thermal properties of diatomic molecules in the presence of magnetic and AB fields with improved Kratzer potential
• Effects of Topological Defect on the Energy Spectra and Thermo-magnetic Properties of CO Diatomic Molecule
• Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields
• Approximate energy states and thermal properties of a particle with position-dependent mass in external magnetic fields
• Spin symmetry in the Dirac sea derived from the bare nucleon-nucleon interaction