Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators
Miloslav Znojil
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 nonequivalent short-range metric operators Θ = I represented, in Runge-Kutta approximation, by (2R -1)-diagonal matrices.
arXiv:0908.4045•Symmetry Integrability and Geometry Methods and Applications•Aug 27, 2009•7 citations