Exactly Solvable Many-Body Systems and Pseudo-Hermitian Point Interactions

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We study Hamiltonian systems with point interactions and give a systematic description of the corresponding boundary conditions and the spectrum properties for self-adjoint, 𝒫𝒯-symmetric systems and systems with real spectra. The integrability of one dimensional many-body systems with these kinds of point (contact) interactions are investigated for both bosonic and fermionic statistics.

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