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

Maurice de Gosson; Franz Luef

doi:10.1007/s11005-007-0150-6

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

Maurice de Gosson·Franz Luef

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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.

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BibTeX RIS

Maurice de Gosson, Franz Luef. 2007-03-07. Quantum States and Hardy's Formulation of the Uncertainty Principle : a Symplectic Approach. https://doi.org/10.1007/s11005-007-0150-6

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