BOSON INVERSE OPERATORS AND ASSOCIATED COHERENT STATES

Making use of the recently introduced inverses of boson creation and a nnihilation operators, we show that the 'photon-added coherent states' are eigenstates of the operator (($) over cap a(dagger m)($) over cap a ($) over cap a(dagger-m)) and also of the operator (($) over cap a - m ($) over cap a(dagger-1)) with eigenvalue alpha. We discuss comple teness of these states. We obtain another family of photon-added coher ent states which are proportional to ($) over cap a(-m)\alpha), where m is a positive integer and \alpha) is a coherent state. We show that these are the eigenstates of the operator (($) over cap a(-m)($) over cap a(m+1)) with eigenvalue alpha. Analogously, we introduce 'photon-d epleted coherent states', (($) over cap a(dagger-m)\alpha), and show t hat these are the eigenstates of the operator (<($)over <($)over ($) o ver cap a+m ($) over cap a(dagger-1)) with eigenvalue alpha. The condi tions for squeezing and antibunching of photons have also been discuss ed.