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The Green’s functions related to a Dirac electron and its corresponding antiparticle, i.e., the positron submitted to an exponentially decaying magnetic field in (2 + 1) coordinate space are analytically calculated via path integral formalism. The energy spectra for both discrete and continuous phenomena, as well as the corresponding normalized eigenspinors are extracted following this approach from the known Morse potential propagator. The interesting properties of the spinors are thus deduced after symmetrization of the Green’s functions. Special cases are also considered.

Exact path integral solutions of Dirac wave equation for an exponentially decaying magnetic field