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Canonical-covariant Wigner function in polar form.

T Hakioğlu1

  • 1Department of Physics, Bilkent University, Ankara, Turkey. hakioglu@theory.hep.anl.gov

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|January 5, 2001
PubMed
Summary

This study explores the two-dimensional Wigner function in polar coordinates, deriving its covariance properties under affine canonical transformations for quantum mechanics applications.

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Area of Science:

  • Quantum mechanics
  • Mathematical physics

Background:

  • The Wigner function is a key tool for representing quantum states in phase space.
  • Understanding its behavior under transformations is crucial for theoretical development.

Purpose of the Study:

  • To analyze the two-dimensional Wigner function in polar canonical coordinates.
  • To derive covariance properties under affine canonical transformations.

Main Methods:

  • Utilizing polar canonical coordinates for Wigner function representation.
  • Applying group theory to derive transformation properties.

Main Results:

  • The covariance properties of the two-dimensional Wigner function in polar coordinates are established.
  • The research provides a mathematical framework for analyzing quantum systems under transformations.

Conclusions:

  • The derived covariance properties offer new insights into the phase space representation of quantum states.
  • This work contributes to the foundational understanding of quantum mechanics and its mathematical formalisms.

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