Pseudo-Hermiticity and weak pseudo-Hermiticity: Equivalence of complementarity and the coordinate transformations in position-dependent mass

TL;DR

This paper explores the relationship between pseudo-Hermiticity and weak pseudo-Hermiticity, showing their equivalence through coordinate transformations, which clarifies their complementarity in quantum mechanics with position-dependent mass.

Contribution

It demonstrates that the concepts of pseudo-Hermiticity and weak pseudo-Hermiticity are equivalent via coordinate transformations, providing a unified understanding of their complementarity.

Findings

Pseudo-Hermiticity and weak pseudo-Hermiticity are equivalent.

Coordinate transformations unify the concepts.

Clarifies the mathematical structure of position-dependent mass systems.

Abstract

The complementarity between the twin concepts of pseudo-Hermiticity and weak pseudo-Hermiticity, established by Bagchi and Quesne [Phys. Lett. A 301 (2002) 173-176], can be understood in terms of coordinate transformations.