Two-dimensional Susy−pseudo-hermiticity without Separation of Variables

We study SUSY −intertwining for non-Hermitian Hamiltonians with complex supercharges. Special emphasis is given to the two-dimensional generalized (singular) Morse potential. This model does not allow for separation of variables nevertheless a part of its spectrum and eigenfunctions can be constructed. The spectrum includes both complex conjugated energy pairs and non-paired complex energies for states linear superpositions of zero modes of the intertwining operator. The two methods, already studied for the investigation of the Hermitian model SUSY −separation of variables and two-dimensional shape invariance are complexified.