International Journal of Theoretical Physics

, Volume 50, Issue 5, pp 1614–1627 | Cite as

Cryptohermitian Hamiltonians on Graphs. II. Hermitizations

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Abstract

In the second step of our systematic study of non-Hermitian quantum graphs simplified via their discretization and possessing real (i.e., in principle, observable) spectra we show how the related Hamiltonian H may be assigned either a pseudometric \(\mathcal{P}\) and/or metric Θ. Our two alternative constructions convert the Hamiltonian in question into the operator which becomes Hermitian either in a formal, ad hoc Krein/Pontryagin space and/or in one of available standard quantum-mechanical Hilbert spaces, respectively.

Keywords

Quantum graphs Non-Hermitian interactions Pseudometrics and metrics Runge-Kutta approximation Cryptohermitian lattices Krein Prontryagin and hilbert space Hermitization 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Nuclear Physics Institute ASCRŘežCzech Republic

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