On the Real Spectra of Calogero Model with Complex Coupling

TL;DR

This paper investigates the eigenvalues of the Calogero model with complex coupling, revealing that certain eigenstates have real energies despite the model's non-invariance under PT symmetry.

Contribution

It demonstrates that eigenstates with zero generalized angular momentum in the complex Calogero model can have real spectra, even without PT invariance.

Findings

Eigenstates with zero angular momentum have real energies.

The model's non-PT-invariance does not preclude real spectra for specific states.

Provides insights into non-Hermitian quantum models with real spectra.

Abstract

We study the eigenvalue problem of the rational Calogero model with the coupling of the inverse-square interaction as a complex number. We show that although this model is manifestly non-invariant under the combined parity and time-reversal symmetry ${\cal{PT}}$, the eigenstates corresponding to the zero value of the generalized angular momentum have real energies.