Solving simultaneously Dirac and Ricatti equations

We analyse the behaviour of the Dirac equation in d = 1 + 1 with Lorentz sc alar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization m ethod in order to enlarge the restricted class of solvable problems. To be precise, it suffices to integrate a Ricatti equation to construct one-param eter families of solvable potentials. To illustrate the procedure in a simp le but relevant context, we resort to a model which has proved useful in sh owing the phenomenon of fermion number fractionalization.