Spectral singularity and non-Hermitian PT-symmetric extension of an AN 1-type Calogero model without confining potential

Abstract

We consider non-Hermitian PT-symmetric deformation of an AN 1-type Calogero model without confining potential to investigate the possible existence of spectral singularity. By considering the Wronskian between asymptotic incoming and outgoing scattering state wavefunctions, we found that there exists no spectral singularity in this model. We further explicitly show that the transmission coefficient vanishes and the reflection coefficient becomes unity for all values of the energy in such a momentum-dependent non-Hermitian PT-symmetric model. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to Quantum physics with non-Hermitian operators. © 2012 IOP Publishing Ltd.