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Harmonic oscillator with complex frequency

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Il Nuovo Cimento B (1971-1996)

Summary

In the present paper we study the problem of the harmonic oscillator with complex frequency. A special case of this problem is the determination of the eigenvalues and eigenfunctions of the squeeze operator in quantum optics. The Hamilton operator of the complex harmonic oscillator is non-Hermitian and its study leads to the Lie-admissible theory. Because of the complex frequency the eigenvalues of the energy are complex numbers and the partition function of Boltzman and the free energy of Helmholtz are complex functions. Especially the imaginary part of the free energy describes the metastable states.

Riassunto

In questo lavoro si studia il problema dell’oscillatore armonico con frequenza complessa. Un caso speciale di questo problema è la determinazione degli autovalori e delle autofunzioni dell’operatore di schiacciamento nell’ottica quantistica. L’operatore di Hamilton dell’oscillatore armonico complesso è non hermitiano e il suo studio porta alla teoria ammissibile secondo Lie. A causa della frequenza complessa, gli autovalori dell’energia sono numeri complessi e la funzione di partizione di Boltzmann e l’energia libera di Helmholtz sono funzioni complesse. Specialmente la parte immaginaria della energia libera descrive gli stati metastabili.

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Authors and Affiliations

  1. Department of Physics, University of Patras, Patras, Greece

    A. Jannussis & E. Skuras

  2. Institute for Basic Research, 96 Preccott Str., 02138, Cambridge, MA

    A. Jannussis

Authors
  1. A. Jannussis
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  2. E. Skuras
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Jannussis, A., Skuras, E. Harmonic oscillator with complex frequency. Nuov Cim B 94, 29–36 (1986). https://doi.org/10.1007/BF02721575

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  • DOI: https://doi.org/10.1007/BF02721575

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