Non linear pseudo-bosons versus hidden Hermiticity

TL;DR

This paper compares hidden Hermiticity and non-linear pseudo-bosons, establishing their formal equivalence and exploring their applications in quantum mechanics under general assumptions.

Contribution

It demonstrates the formal equivalence between hidden Hermiticity and non-linear pseudo-bosons, providing a unified framework for their application in quantum mechanics.

Findings

Established the formal equivalence between hidden Hermiticity and non-linear pseudo-bosons.

Provided examples demonstrating their applicability in quantum mechanics.

Discussed the general assumptions under which this equivalence holds.

Abstract

The increasingly popular concept of a hidden Hermiticity of operators (i.e., of their Hermiticity with respect to an {\it ad hoc} inner product in Hilbert space) is compared with the recently introduced notion of {\em non-linear pseudo-bosons}. The formal equivalence between these two notions is deduced under very general assumptions. Examples of their applicability in quantum mechanics are discussed.