Exact closed-form solutions of the Dirac equation for a class of effective Morse potentials - de Castro, A. S.; Hott, M. (American Institute of Physics (AIP), 2004)
Exact bounded solutions for a fermion subject to exponential scalar potential in 1 + 1 dimensions are found in closed form. We discuss the existence of zero modes which are related to the ultrarelativistic limit of the Dirac equation and are responsible for the induction of a fractional fermion number on the vacuum.