Bounded solutions of fermions in the background of mixed vector-scalar Pöschl-Teller-like potentials

Abstract

The problem of a fermion subject to a convenient mixing of vector and scalar potentials in a two-dimensional space-time is mapped into a Sturm-Liouville problem. For a specific case which gives rise to an exactly solvable effective modified Pöschl-Teller potential in the Sturm-Liouville problem, bound-state solutions are found. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail and some unusual results are revealed. The Dirac delta potential as a limit of the modified P% öschl-Teller potential is also discussed. The problem is also shown to be mapped into that of massless fermions subject to classical topological scalar and pseudoscalar potentials.

arXiv comment10 pages, 1 figure

References in corpus (14)

• Pseudo-spin as a Relativistic Symmetry
• Pseudospin symmetry and the relativistic harmonic oscillator
• On the Relativistic Foundations of Pseudospin Symmetry in Nuclei
• A Relativistic Symmetry in Nuclei
• Pseudospin symmetry and its approximation in real nuclei
• The Isospin Asymmetry in the Pseudo-spin Dynamical Symmetry
• Pseudospin symmetry as a relativistic dynamical symmetry in the nucleus
• Effect of tensor couplings in a relativistic Hartree approach for finite nuclei
• The supersymmetric modified Poschl-Teller and delta-well potentials
• Trapping neutral fermions with kink-like potentials
• Exact closed-form solutions of the Dirac equation with a scalar exponential potential
• Confinement of fermions by mixed vector-scalar linear potentials in two-dimensional space-time
• Exact solution for a fermion in the background of a scalar inversely linear potential
• Bounded solutions of fermions in the background of mixed vector-scalar inversely linear potentials

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• Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling
• Dirac bound states of anharmonic oscillator in external fields
• Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
• Stationary states of fermions in a sign potential with a mixed vector-scalar coupling
• Confinement of fermions in tachyon matter
• Unsuitable use of spin and pseudospin symmetries with a pseudoscalar Cornell potential
• Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics