Classical Trajectories of the Continuum States of the $\mathcal{P}\mathcal{T}$ symmetric Scarf II potential

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 $\mathcal{P}\mathcal{T}$ 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.

7 pages, 8 figures

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Factorizations of one dimensional classical systems
• Spontaneous Breaking of Classical PT Symmetry

Cited by in corpus (2)

• Reciprocity and unitarity in scattering from a non-Hermitian complex PT-symmetric potential
• Spectral singularity and deep multiple minima in the reflectivity in non-Hermitian (complex) Ginocchio potential