Complexified von Roos Hamiltonian's η-weak-pseudo-Hermiticity, isospectrality and exact solvability

Abstract

A complexified von Roos Hamiltonian is considered and a Hermitian firstorder intertwining differential operator is used to obtain the related positiondependent mass η-weak-pseudo-HermitianHamiltonians. Using a Liouvilleantype change of variables, the η-weak-pseudo-Hermitian von Roos Hamiltonians Hx are mapped into the traditional Schr¨odinger Hamiltonian form Hq , where exact isospectral correspondence between Hx and Hq is obtained. Under a ‘user-friendly’ position-dependent-mass setting, it is observed that for each exactly solvable η-weak-pseudo-Hermitian reference-Hamiltonian Hq there is a set of exactly solvable η-weak-pseudo-Hermitian isospectral target Hamiltonians Hx . A non-Hermitian PT -symmetric Scarf II and a non- Hermitian periodic-type PT -symmetric Samsonov–Roy potentials are used as reference models and the corresponding η-weak-pseudo-Hermitian isospectral target-Hamiltonians are obtained.