Letters in Mathematical Physics

, Volume 80, Issue 1, pp 69–82

Quantum States and Hardy’s Formulation of the Uncertainty Principle: a Symplectic Approach

Authors

    • Faculty of MathematicsUniversity of Vienna
  • Franz Luef
    • Faculty of MathematicsUniversity of Vienna
Article

DOI: 10.1007/s11005-007-0150-6

Cite this article as:
de Gosson, M. & Luef, F. Lett Math Phys (2007) 80: 69. doi:10.1007/s11005-007-0150-6

Abstract

We express the condition for a phase space Gaussian to be the Wigner distribution of a mixed quantum state in terms of the symplectic capacity of the associated Wigner ellipsoid. Our results are motivated by Hardy’s formulation of the uncertainty principle for a function and its Fourier transform. As a consequence we are able to state a more general form of Hardy’s theorem.

Mathematics Subject Classification (2000)

81S1081S3037J05

Keywords

Hardy’s uncertainty principleWigner distributiondensity operatorpositivity

Copyright information

© Springer 2007