A bounded version of bosonic creation and annihilation operators and their related quasi-coherent states

TL;DR

This paper introduces a bounded operator related to the annihilation operator to define quasi-coherent states, enabling a modified harmonic oscillator analysis with potential advantages over traditional unbounded operator frameworks.

Contribution

It presents a novel bounded operator construction for quasi-coherent states, expanding the mathematical framework of coherent state theory.

Findings

Defined quasi-coherent states as quasi-eigenstates of a bounded operator

Constructed a modified harmonic oscillator based on this bounded operator

Analyzed the algebraic dynamics of the new oscillator model

Abstract

Coherent states are usually defined as eigenstates of an unbounded operator, the so-called annihilation operator. We propose here possible constructions of {\em quasi-coherent states}, which turn out to be {\em quasi} eigenstate of a \underline{bounded} operator related to an annihilation-like operator. We use this bounded operator to construct a sort of modified harmonic oscillator and we analyze the dynamics of this oscillator from an algebraic point of view.