International Journal of Theoretical Physics

, Volume 36, Issue 11, pp 2349–2369 | Cite as

Rigged Hilbert spaces and time asymmetry: The case of the upside-down simple harmonic oscillator

  • Morio Castagnino
  • Roberto Diener
  • Luis Lara
  • Gabriel Puccini


The upside-down simple harmonic oscillator system is studied in the contexts of quantum mechanics and classical statistical mechanics. It is shown that in order to study in a simple manner the creation and decay of a physical system by way of Gamow vectors we must formulate the theory in a time-asymmetric fashion, namely using two different rigged Hilbert spaces to describe states evolving toward the past and the future. The spaces defined in the contexts of quantum and classical statistical mechanics are shown to be directly related by the Wigner function.


Hilbert Space Wigner Function Liouville Equation Liouvillian Operator Generalize Eigenvector 
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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Morio Castagnino
    • 1
    • 2
    • 3
  • Roberto Diener
    • 2
  • Luis Lara
    • 3
  • Gabriel Puccini
    • 3
  1. 1.IAFEBuenos AiresArgentina
  2. 2.Departmento de FísicaUniversidad de Buenos AiresArgentina
  3. 3.Facultad de Ciencias ExactasIngeniería y AgrimensuraRosarioArgentina

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