Non-Hermitian von Roos Hamiltonian’s η-weak-pseudo-Hermiticity and exact solvability

A complexified von Roos Hamiltonian is considered and a Hermitian first-order intertwining differential operator is used to obtain the related position dependent mass η-weak-pseudo-Hermitian Hamiltonians. Two ”user -friendly” reference-target maps are introduced to serve for exactsolvability of some non-Hermitian η-weak-pseudo-Hermitian position dependent mass Hamiltonians. A non-Hermitian PT -symmetric Scarf II and a non-Hermitian periodic-type PT -symmetric Samsonov-Roy potentials are used as reference models in a ”user-friendly” reference-target map and the corresponding isospectral Hamiltonians are obtained. It is observed that for each exactly-solvable reference Hamiltonian there is a corresponding set of exactly-solvable target Hamiltonians. PACS numbers: 03.65.Ge, 03.65.Fd, 03.65.Ca