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The Dynamical Problem for a Non Self-adjoint Hamiltonian

  • Fabio BagarelloEmail author
  • Miloslav Znojil
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 221)

Abstract

After a compact overview of the standard mathematical presentations of the formalism of quantum mechanics using the language of C*- algebras and/or the language of Hilbert spaces we turn attention to the possible use of the language of Krein spaces.I n the context of the so-called three-Hilbert-space scenario involving the so-called PT-symmetric or quasi- Hermitian quantum models a few recent results are reviewed from this point of view, with particular focus on the quantum dynamics in the Schrödinger and Heisenberg representations.

Keywords

Metrics in Hilbert spaces hermitizations of a Hamiltonian 

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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Dieetcam, Facoltà di IngegneriaUniversità di PalermoPalermoItaly
  2. 2.Nuclear Physics Institute ASCRŘežCzech Republic

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