Bound and Scattering States of Extended Calogero Model with an Additional 𝒫𝒯 Invariant Interaction*

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Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but 𝒫𝒯 (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameters differ from each other in the presence of 𝒫𝒯 invariant interaction.

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