First-Order Intertwining Operators with Position Dependent Mass and η-Weak-Pseudo-Hermiticity Generators

Abstract

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of η-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target η-weak-pseudo-Hermitian PDM— Hamiltonians’ map is suggested. Some η-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-levels crossing and flown-away states phenomena are reported for the resulting Scarf II spectrum. Some of the corresponding η-weak-pseudo-Hermitian Scarf II- and periodic-type-isospectral models (PT -symmetric and non-PT -symmetric) are given as products of the reference-target map.