  A supersymmetric one-dimensional matrix procedure similar to relationships of
the same type between Dirac and Schrodinger equations in particle physics is
described at the general level. 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 to molecular diffraction
in evanescent waves over nanostructured surfaces
