On The Connection Between Dirac And Ricatti Equations

We analyse the behaviour of the Dirac equation in d = 1 + 1 with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to enlarge the restricted class of solvable problems. To be precise, it suffices to integrate a Ricatti equation to construct one-parameter families of solvable potentials. To illustrate the procedure in a simple but relevant context, we resort to a model which has proved useful in showing the phenomenon of fermion number fractionalization. 1. Introduction. When solving the Dirac equation in d = 1 + 1 with Lorentz scalar potential, the underlying supersymmetric structure is crucial. As the system provides a physical realization of supersymmetric quantum mechanics (susy qm henceforth), the problem reduces itself to a pair of Schrodinger-like hamiltonians related by means of supersymmetry. In doing so, both operators share identical energy spectra u..