Non-Hermitian oscillator-like Hamiltonians and $λ$-coherent states revisited

Abstract

Previous $λ$-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 $λ$-states lead to new families of coherent states according to the DOCS, AOCS and MUCS points of view.