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

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.