On the Real Spectra of Calogero Model with Complex Coupling
Pijush K. Ghosh, Kumar S. Gupta

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 , the eigenstates corresponding to the zero value of the generalized angular momentum have real energies.
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