Classical Trajectories of the Continuum States of the ${\cal{PT}}$ symmetric Scarf II potential

TL;DR

This paper derives exact classical trajectories and momenta for the continuum states of the ${ m PT}$-symmetric Scarf II potential, revealing classical analogues of quantum spectral singularities.

Contribution

It applies a factorization technique to obtain analytical classical solutions for a non-Hermitian ${ m PT}$-symmetric potential, linking quantum spectral features to classical behavior.

Findings

Classical trajectories are analytically obtained for the continuum states.

Spectral singularities have interesting classical analogues.

Classical behavior reflects quantum spectral properties.

Abstract

We apply the factorization technique developed by Kuru et. al. [Ann. Phys. {\bf 323} (2008) 413] to obtain the exact analytical classical trajectories and momenta of the continuum states of the non Hermitian but ${\cal{PT}}$ symmetric Scarf II potential. In particular, we observe that the strange behaviour of the quantum version at the spectral singularity has an interesting classical analogue.