Bound states of the two-dimensional Dirac equation for an energy-dependent hyperbolic Scarf potential

Abstract

We study the two-dimensional massless Dirac equation for a potential that is allowed to depend on the energy and on one of the spatial variables. After determining a modified orthogonality relation and norm for such systems, we present an application involving an energy-dependent version of the hyperbolic Scarf potential. We construct closed-form bound state solutions of the associated Dirac equation.

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• The zero-energy state in graphene in a high magnetic field
• Two-dimensional Dirac particles in a Pöschl-Teller waveguide
• Spectrally isomorphic Dirac systems: graphene in electromagnetic field
• On zero energy states in graphene
• Construction of zero energy states in graphene through the supersymmetry formalism

Cited by in corpus (2)

• Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart
• Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry