2013/06/20 by Ananya Ghatak, Raka Dona Ray Mandal, Bhabani Prasad Mandal
Physics and Astronomy · #Bound state #Gravitational singularity #Hermitian matrix #Invariant (physics) #Mathematical analysis #Mathematical physics #Maxima and minima #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Reciprocity (cultural anthropology) #Scattering #Singularity #quant-ph
paper · pdf · doi:10.1016/j.aop.2013.06.008
published as Annals of Physics, 336, 540 (2013) · 17 pages, 6 figures
openalex publication_date 2013/06/20 · arxiv created 2013/10/29 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We complexify a 1-d potential which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters becomes imaginary. For one PT-symmetric case we have entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from left (or right) at certain discrete energies. The penetrating states in the other PT-symmetric configuration are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. Presence of MSS and reflectionlessness are also discussed for the free states in the later case.