Electron propagator with vector and scalar energy-dependent potentials in (2+1)-dimensional space–time

Abstract

We have studied the effect of energy-dependent potentials for the relativistic spinning particle using the formalism for supersymmetric path integrals. That leaves behind a new normalization of wave function, which is examined via the Dirac equation and can be confirmed by Feynman’s path integral method. Based on two important examples, Coulomb and Harmonic oscillator potentials, we find that the frequency and the Coulomb’s constant are dependent on spectral parameters. The propagator is calculated and the energy eigenvalues with their corresponding eigenfunctions are deduced.