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We consider the inequivalent quantizations of a $N$-body rational Calogeromodel with a Coulomb type interaction. It is shown that for certain range ofthe coupling constants, this system admits a one-parameter family ofself-adjoint extensions. We analyze both the bound and scattering state sectorsand find novel solutions of this model. We also find the ladder operators forthis system, with which the previously known solutions can be constructed.

Inequivalent quantization of the rational Calogero model with a Coulomb type interaction