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arXiv · math-ph/9810022

Solving simultaneously Dirac and Ricatti equations

Javier Casahorrán
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Abstract

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.

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Javier Casahorrán. 1998-10-01. Solving simultaneously Dirac and Ricatti equations. https://doi.org/10.2991/jnmp.1998.5.4.4

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