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Uncertainty Principle, Phase Space Ellipsoids and Weyl Calculus

Maurice A. de Gosson

Published Jan 1, 2006• 13 citations

Abstract

We state a precise form of the uncertainty principle in terms of phase space ellipsoids, which we then express in terms of the symplectic capacity of phase space ellipsoids. We apply our approach to the study of the positivity of the Wigner transform of a pure quantum state, and of that of the Weyl operator associated to the average of a positive symbol over a phase space ellipsoid.

DOI: 10.1007/3-7643-7514-0_9

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