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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 usethis bounded operator to construct a sort of modified harmonic oscillator andwe analyze the dynamics of this oscillator from an algebraic point of view.

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