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

TL;DR

This paper investigates bound states of the two-dimensional massless Dirac equation with an energy-dependent hyperbolic Scarf potential, deriving modified orthogonality relations and providing explicit solutions.

Contribution

It introduces a modified orthogonality relation for energy-dependent potentials and constructs explicit bound state solutions for a specific energy-dependent potential.

Findings

Derived a modified orthogonality relation and norm for energy-dependent systems.

Constructed closed-form bound state solutions for the energy-dependent hyperbolic Scarf potential.

Demonstrated the applicability of the method to a specific class of energy-dependent potentials.

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.