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Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators

Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators

One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our...

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Main Author: Znojil, M.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/149110
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spelling irk-123456789-1491102019-02-20T01:26:12Z Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators Znojil, M. One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv:0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain non-equivalent short-range metric operators Θ ≠ I represented, in Runge-Kutta approximation, by (2R–1)-diagonal matrices. 2009 Article Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81U20; 46C15; 81Q10; 34L25; 47A40; 47B50 http://dspace.nbuv.gov.ua/handle/123456789/149110 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H ≠ H† is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space formulation of quantum theory is reviewed as explaining the unitarity of scattering. Our recent paper on bound states [Znojil M., SIGMA 5 (2009), 001, 19 pages, arXiv:0901.0700] is complemented by the text on scattering. An elementary example illustrates the feasibility of the resulting innovative theoretical recipe. A new family of the so called quasilocal inner products in Hilbert space is found to exist. Constructively, these products are all described in terms of certain non-equivalent short-range metric operators Θ ≠ I represented, in Runge-Kutta approximation, by (2R–1)-diagonal matrices.
format Article
author Znojil, M.
spellingShingle Znojil, M.
Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Znojil, M.
author_sort Znojil, M.
title Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
title_short Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
title_full Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
title_fullStr Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
title_full_unstemmed Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
title_sort cryptohermitian picture of scattering using quasilocal metric operators
publisher Інститут математики НАН України
publishDate 2009
url http://dspace.nbuv.gov.ua/handle/123456789/149110
citation_txt Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT znojilm cryptohermitianpictureofscatteringusingquasilocalmetricoperators
first_indexed 2023-05-20T17:32:21Z
last_indexed 2023-05-20T17:32:21Z
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