Weak-Pseudo-Hermiticity of Non-Hermitian Hamiltonians with Position-Dependent Mass

TL;DR

This paper extends the concept of eta-weak-pseudo-Hermiticity to non-Hermitian Hamiltonians with position-dependent mass, providing a method to construct such Hamiltonians and exploring specific potential cases.

Contribution

It introduces a new framework for eta-weak-pseudo-Hermiticity applicable to position-dependent mass systems, expanding the class of non-Hermitian Hamiltonians studied.

Findings

Constructed non-Hermitian Hamiltonians with position-dependent mass

Derived specific potential cases within the new framework

Provided a method for generating such Hamiltonians

Abstract

We extend the definition of eta-weak-pseudo-Hermiticity to the class of potentials endowed with position-dependent mass. The construction of non-Hermitian Hamiltonians through some generating function are obtained. Special cases of potentials are thus deduced.