We prove a sharp version of the Hardy uncertainty principle for Schr\"odinger equations with external bounded electromagnetic potentials, based on logarithmic convexity properties of Schr\"odinger evolutions. We provide, in addition, an example of a real electromagnetic potential which produces the existence of solutions with critical gaussian decay, at two distinct times.
Sharp Hardy uncertainty principle and gaussian profiles of covariant Schrödinger evolutions
CASSANO, BIAGIO;
2015
Abstract
We prove a sharp version of the Hardy uncertainty principle for Schr\"odinger equations with external bounded electromagnetic potentials, based on logarithmic convexity properties of Schr\"odinger evolutions. We provide, in addition, an example of a real electromagnetic potential which produces the existence of solutions with critical gaussian decay, at two distinct times.File in questo prodotto:
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