Non-Hermitian oscillator-like Hamiltonians and $\lambda$-coherent states revisited

TL;DR

This paper revisits non-Hermitian oscillator-like Hamiltonians with a new scalar product to establish their self-adjointness, leading to the development of new families of coherent states from various perspectives.

Contribution

It introduces a new scalar product framework for non-Hermitian Hamiltonians, enabling the construction of novel $oldsymbol{ extit{ ext{lambda}}}$-coherent states and expanding the understanding of their properties.

Findings

Revised scalar product restores self-adjointness of non-Hermitian Hamiltonians.

New families of coherent states are constructed based on different coherence criteria.

The approach enhances the theoretical framework for non-Hermitian quantum systems.

Abstract

Previous $\lambda$-deformed {\it non-Hermitian} Hamiltonians with respect to the usual scalar product of Hilbert spaces dealing with harmonic oscillator-like developments are (re)considered with respect to a new scalar product in order to take into account their property of self-adjointness. The corresponding deformed $\lambda$-states lead to new families of coherent states according to the DOCS, AOCS and MUCS points of view.