Position-dependent mass Dirac equation and local Fermi velocity

Abstract We present a new approach to study the one-dimensional Dirac equation in background of position-dependent mass m . Taking Fermi velocity v f be local variable, we explore resulting structure coupled equations and arrive at an interesting constraint turning out inverse square address several solvable systems that include free particle, shifted harmonic oscillator, Coulomb nonpolynomial potentials. In particular, supersymmetric quantum mechanics context, upper partner effective potential yields form for quadratic functional choice velocity.