Abstract
The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinus-square potential respectively. These models are well known to be integrable and solvable. Here we extend the Calogero and Sutherland Hamiltonians by means of new interactions which are PT-symmetric but not self-adjoint. Some of these new interactions lead to integrable PT-symmetric Hamiltonians. The algebraic properties of these interactions reveal further that they are also solvable. In addition, we consider PT-symmetric interactions which lead to new quasi-exactly-solvable deformations of the Calogero and Sutherland Hamiltonians.
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