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The Dynamical Problem for a Non Self-adjoint Hamiltonian

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Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 221))

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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.

Mathematics Subject Classification (2000).Primary 47B50; Secondary 81Q65 47N50 81Q12 47B36 46C20.

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Author information

Authors and Affiliations

  1. Dieetcam, Facoltà di Ingegneria, Università di Palermo, I-90128, Palermo, Italy

    Fabio Bagarello

  2. Nuclear Physics Institute ASCR, 250 68, Řež, Czech Republic

    Miloslav Znojil

Authors
  1. Fabio Bagarello
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  2. Miloslav Znojil
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Corresponding author

Correspondence to Fabio Bagarello .

Editor information

Editors and Affiliations

  1. , Abt. Mathematik V, Universität Ulm, Ulm, 89069, Germany

    Wolfgang Arendt

  2. Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA

    Joseph A. Ball

  3. Institut für Mathematik, AG Modellierung, Numerik und, TU Berlin, Straße des 17 Juni 136, Berlin, 10623, Berlin, Germany

    Jussi Behrndt

  4. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Karl-Heinz Förster

  5. Fak. II Mathematik & Naturwissenschaften, Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Volker Mehrmann

  6. , Institut für Mathematik, TU Ilmenau, Weimarer Str. 25, Ilmenau, 98693, Thüringen, Germany

    Carsten Trunk

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Bagarello, F., Znojil, M. (2012). The Dynamical Problem for a Non Self-adjoint Hamiltonian. In: Arendt, W., Ball, J., Behrndt, J., Förster, KH., Mehrmann, V., Trunk, C. (eds) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0297-0_6

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