Pseudo supersymmetric Partners for the Generalized Swanson Model

New non Hermitian Hamiltonians are generated, as isospectral partners of the generalized Swanson model, viz., H− = A†A + αA2 + βA† 2, where α , β are real constants, with α 6= β, and A† and A are generalized creation and annihilation operators. It is shown that the initial Hamiltonian H−, and its partner H+, are related by pseudo supersymmetry, and they share all the eigen energies except for the ground state. This pseudo supersymmetric extension enlarges the class of non Hermitian Hamiltonians H±, related to their respective Hermitian counterparts h±, through the same similarity transformation operator ρ : H± = ρ −1 h± ρ. The formalism is applied to the entire class of shape-invariant models. PACS Numbers : 03.65.-w, 03.65.Ca, 03.65.Ge