Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators

0333958 - ÚJF 2010 RIV UA eng J - Journal Article
Znojil, Miloslav
Cryptohermitian Picture of Scattering Using Quasilocal Metric Operators.
Symmetry, Integrability and Geometry: Methods and Applications. Roč. 5, - (2009), 085/1-085/21. ISSN 1815-0659
R&D Projects: GA MŠMT LC06002; GA ČR GA202/07/1307
Institutional research plan: CEZ:AV0Z10480505
Keywords : cryptohermitian observables * unitary scattering * Runge-Kutta discretization
Subject RIV: BE - Theoretical Physics
Impact factor: 0.789, year: 2009

One-dimensional unitary scattering controlled by non-Hermitian (typically, PT-symmetric) quantum Hamiltonians H not equal 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 Theta not equal I represented, in Runge-Kutta approximation, by (2R-1)-diagonal matrices.
Permanent Link: http://hdl.handle.net/11104/0178811