Riccati non hermeticity with application to the Morse potential

A supersymmetric one-dimensional matrix procedure, similar to the relationships of the same type between Dirac and Schrodinger equations in particle physics, is described in the general terms. By this means, we are able to introduce a non hermitic 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 non hermitic Morse problem. A possible application is the molecular diffraction in evanescent waves over nano structured surfaces. (Author)