A generalized non-Hermitian oscillator Hamiltonian, NN-fold supersymmetry and position-dependent mass models

A generalized non-Hermitian oscillator Hamiltonian is proposed that consists of additional linear terms which break PTPT-symmetry explicitly. The model is put into an equivalent Hermitian form by means of a similarity transformation and the criterion of NN-fold supersymmetry with a position-dependent mass is shown to reside in it.