The Role of Scalar Product and Wigner Distribution in Optical and Quantum Mechanical Measurements

  • K. Wódkiewicz
Part of the NATO ASI Series book series (volume 110)


The concept of phase-space measurement in Acoustics or Optics is much older than the now standard phase-space description of classical mechanics. A musical score offers perhaps the oldest and the simplest example of a phase space representation of an acoustical signal in the time and frequency domain.


Wigner Function WIGNER Distribution Musical Score WIGNER Distribution Function Phase Space Representation 
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Copyright information

© Plednum Press, New York 1984

Authors and Affiliations

  • K. Wódkiewicz
    • 1
    • 2
  1. 1.Department of Physics and AstronomyUniversity of RochesterRochesterUSA
  2. 2.Institute of Theoretical PhysicsWarsaw UniversityWarsawPoland

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