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Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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One-dimensional unitary scattering controlled by non-Hermitian (typically, $\mathcal{PT}$-symmetric) quantum Hamiltonians $H\neq H^\dagger$ 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 [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 $\Theta\neq I$ represented, in Runge–Kutta approximation, by $(2R-1)$-diagonal matrices.
Keywords: cryptohermitian observables; unitary scattering; Runge–Kutta discretization; quasilocal metric operators. 
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     author = {Miloslav Znojil},
     title = {Cryptohermitian {Picture} of {Scattering} {Using} {Quasilocal} {Metric} {Operators}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a84/}
}
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Miloslav Znojil. Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a84/

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