From Equations of Motion to Canonical Commutation Relations: Classical and Quantum Systems

  • V. I. Man’ko
  • G. Marmo
  • F. Zaccaria


We consider equations of motion for classical and quantum systems. It is shown that they do not determine uniquely the canonical commutation relations, neither at the classical level, nor at the quantum level. By using some of the alternative commutation relations as deformed ones, we consider the description of deformed systems, classical and quantum. In particular, by using deformed oscillators we deal with photon statistics in nonlinear coherent states and possible influence of deformations on electrostatics.


Harmonic Oscillator Coherent State Commutation Relation Free Particle Hamiltonian Function 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • V. I. Man’ko
    • 1
    • 2
  • G. Marmo
    • 1
  • F. Zaccaria
    • 1
  1. 1.Dipartimento di Scienze FisicheUniversitá di Napoli “Federico II”, Instituto Nazionale di Fisica Nucleare, Sezione di NapoliNapoliItaly
  2. 2.Lebedev Physical InstituteMoscowRussia

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