On PT-symmetric extensions of the Calogero and Sutherland models

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. They 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 further reveal that they are solvable as well. We also consider PT-symmetric interactions which lead to a new quasi-exactly solvable deformation of the Calogero and Sutherland Hamiltonians.

arXiv comment10 pages, LaTeX

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Cited by in corpus (4)

• A note on the integrability of non-Hermitian extensions of Calogero-Moser-Sutherland models
• Spectral singularity and non-Hermitian PT-symmetric extension of $A_{N-1}$ type Calogero model without confining potential
• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models
• Calogero-like model without rearrangement symmetry