On PT-symmetric extensions of the Calogero model

The original Calogero model describes N quantum particles on the line interacting pairwise through a inverse square potential. It is well known to be integrable and solvable. Here we extend the Calogero Hamiltonian 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 further reveal that they are solvable as well. We also consider a PTsymmetric interaction which leads to a new quasi exactly solvable deformation of the Calogero Hamiltonian. [email protected] [email protected]