ua nt - p h / 99 08 04 5 v 1 1 3 A ug 1 99 9 A novel realization of the Calogero - Moser scattering states as coherent states

A novel realization is provided for the scattering states of the N -particle Calogero-Moser Hamiltonian. They are explicitly shown to be the coherent states of the singular oscillators of the Calogero-Sutherland model. Our algebraic treatment is straightforwardly extendable to a large number of few and many-body interacting systems in one and higher dimensions. PACS: 03.65.-w, 03.65.Ge Typeset using REVTEX ∗[email protected] †[email protected] 1 The N -body Calogero-Sutherland model (CSM), containing harmonic and inverse-square interactions, has been the subject of intense investigation, since its inception [1,2]. Its quantum integrability, exact solvability and ability to capture the universal aspects of diverse physical phenomena [3], has made this model applicable to areas of physics, ranging from, fluid dynamics [4], quantum Hall effect [5], to gauge theories [6]. The many-particle Calogero-Moser model (CMM) [1,7], having only pair-wise inversesquare interactions between particles, has also been studied extensively in the context of novel statistics [8] and recently, black hole physics [9]. In this note, we give a novel realization of the scattering eigenstates of this model as coherent states of the Calogero-Sutherland singular oscillators. This, not only establishes a connection between the wave functions of these two interacting many-body systems, but also provides relationship between scattering and bound state problems. Our algebraic procedure is straightforwardly extendable to a large class of few and many-particle systems, both in one and higher dimensions. The CSM Hamiltonian (h̄ = m = ω = 1), HCSM = − 1 2 N ∑