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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2009 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2009
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149110 |
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| Цитувати: | Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149110 |
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dspace |
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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 |
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AT znojilm cryptohermitianpictureofscatteringusingquasilocalmetricoperators |
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2023-05-20T17:32:21Z |
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2023-05-20T17:32:21Z |
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