de Gosson, Maurice A.;Luef, Franz

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

Lett. Math. Phys. Vol.80 No.1 (2007) p.69-82, MR2314845

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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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