Riccati nonhermiticity with application to the Morse potential

Abstract

A supersymmetric one-dimensional matrix procedure, similar to the relationships of the same type between Dirac and Schrödinger equations in particle physics, is described in the general terms. By this means, we are able to introduce a nonhermitic Hamiltonian having the imaginary part proportional to the solution of a Riccati equation of the Witten type. The procedure is applied to the exactly solvable Morse potential introducing, in this way, the corresponding nonhermitic Morse problem. A possible application is the molecular diffraction in evanescent waves over nanostructured surfaces.