Exact solution of time-independent one-dimensional Dirac equation with position-dependent mass and vector potential of hyperbolic type by generalized SUSY QM approach

In this work, we present a method to solve the one-dimensional time-independent Dirac equation with position-dependent mass using the supersymmetric quantum mechanics (SUSY QM) approach and shape invariance. Choosing the vector potential equal to the mass term and as a hyperbolic function, the Dirac equation is solved exactly, for bound states, by reducing it to a position-dependent Schrödinger-like equation with an energy-dependent effective potential.