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Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
Інший ID:
2000 Mathematics Subject Classification: 81U20; 46C15; 81Q10; 34L25; 47A40; 47B50
Посилання:
Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators / M. Znojil // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 33 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the 5-th Microconference “Analytic and Algebraic Methods V”. The author appreciates the support by the Institutional Research Plan AV0Z10480505, by the MSMT “Doppler Institute” project Nr. LC06002 and by GA ˇ CR grant Nr. 202/07/1307.
Дата:
2009
Переглядів:
360
Завантажень:
205
Анотація:
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.
