Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
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| Creator |
Znojil, M.
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| 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.
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| Date |
2019-02-19T17:27:09Z
2019-02-19T17:27:09Z 2009 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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