Bound and scattering states of extended Calogero model with an additional PT invariant interaction

Abstract

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 parameter differ from each other in the presence of PT invariant interaction.

7 pages, latex, uses czjphys.cls, contributed to the `1st International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physics', Prague, June 16-17, 2003

References in corpus (10)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• A PT-Invariant Potential With Complex QES Eigenvalues
• A family of complex potentials with real spectrum
• Equivalence of the Calogero-Sutherland Model to Free Harmonic Oscillators
• On an exactly solvable $B_N$ type Calogero model with nonhermitian PT invariant interaction
• Exact solution of Calogero model with competing long-range interactions
• Fractional statistics in some exactly solvable Calogero-like models with PT invariant interactions

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