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Series solutions of PT -symmetric Schrödinger equations

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Title: Series solutions of PT -symmetric Schrödinger equations
Authors: Ford, C
Bender, C
Hassanpour, N
Xia, B
Item Type: Journal Article
Abstract: A simple and accurate numerical technique for finding eigenvalues, node structure, and expectation values of ${ \mathcal P }{ \mathcal T }$-symmetric potentials is devised. The approach involves expanding the solution to the Schrödinger equation in series involving powers of both the coordinate and the energy. The technique is designed to allow one to impose boundary conditions in ${ \mathcal P }{ \mathcal T }$-symmetric pairs of Stokes sectors. The method is illustrated by using many examples of ${ \mathcal P }{ \mathcal T }$-symmetric potentials in both the unbroken- and broken-${ \mathcal P }{ \mathcal T }$-symmetric regions.
Issue Date: 7-Feb-2018
Date of Acceptance: 19-Jan-2018
URI: http://hdl.handle.net/10044/1/57353
DOI: https://dx.doi.org/10.1088/2399-6528/aaa953
ISSN: 2399-6528
Publisher: IOP Publishing
Journal / Book Title: Journal of Physics Communications
Volume: 2
Copyright Statement: © 2018 The Author(s). Published by IOP Publishing Ltd. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence . Any further distribution of this work must maintain attribution to the author ( s ) and the title of the work, journal citation and DOI.
Publication Status: Published
Article Number: ARTN 025012
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences