Bound States of the Dirac Equation for a Class of Effective Quadratic Plus Inversely Quadratic Potentials

Abstract

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schroedinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case.

14 pages, 5 figures

References in corpus (6)

• One-dimensional Dirac oscillator in a thermal bath
• Bound states by a pseudoscalar Coulomb potential in 1+1 dimensions
• Confinement of neutral fermions by a pseudoscalar double-step potential in (1+1) dimensions
• Energy bounds for a class of singular potentials and some related series
• Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional space-time
• The Relativistic Linear Singular Oscillator

Cited by in corpus (10)

• Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator
• Trapping neutral fermions with kink-like potentials
• A geometric approach to confining a Dirac neutral particle in analogous way to a quantum dot
• Bounded solutions of neutral fermions with a screened Coulomb potential
• Spectrum of the Relativistic Particles in Various Potentials
• Relativistic confinement of neutral fermions with a trigonometric tangent potential
• A relativistic model of the isotropic three-dimensional singular oscillator
• The peremptory influence of a uniform background for trapping neutral fermions with an inversely linear potential
• On a dynamical symmetry group of the relativistic linear singular oscillator
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential