Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schrödinger equation

Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schrödinger... The phenomenon of the birth of an isolated quantum bound state at the lower edge of the continuum is studied for a particle moving along a discrete real line of coordinates x∈Z. The motion is controlled by a weakly nonlocal 2J-parametric external potential V which is non-Hermitian but PT symmetric. The model is found exactly solvable. The bound states are interpreted as Sturmians. Their closed-form definitions are presented and discussed up to J=7. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schrödinger equation

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Bound states emerging from below the continuum in a solvable PT-symmetric discrete Schrödinger equation

Abstract

The phenomenon of the birth of an isolated quantum bound state at the lower edge of the continuum is studied for a particle moving along a discrete real line of coordinates x∈Z. The motion is controlled by a weakly nonlocal 2J-parametric external potential V which is non-Hermitian but PT symmetric. The model is found exactly solvable. The bound states are interpreted as Sturmians. Their closed-form definitions are presented and discussed up to J=7.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.012127
Publisher site
See Article on Publisher Site

Abstract

The phenomenon of the birth of an isolated quantum bound state at the lower edge of the continuum is studied for a particle moving along a discrete real line of coordinates x∈Z. The motion is controlled by a weakly nonlocal 2J-parametric external potential V which is non-Hermitian but PT symmetric. The model is found exactly solvable. The bound states are interpreted as Sturmians. Their closed-form definitions are presented and discussed up to J=7.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 28, 2017

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