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arXiv · 0908.4045

Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators

Miloslav Znojil
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Abstract

One-dimensional unitary scattering controlled by non-Hermitian (typically, ${\cal PT}$-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 [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 $Θ\neq I$ represented, in Runge-Kutta approximation, by $(2R-1)$-diagonal matrices.

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Miloslav Znojil. 2009-08-31. Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators. https://doi.org/10.3842/sigma.2009.085

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