AMApplied Mathematics2152-7385Scientific Research Publishing10.4236/am.2017.83025AM-74880ArticlesPhysics&Mathematics The Uncertainty Principle in Terms of Isoperimetric Inequalities ThomasSchürmann1*Germaniastra?e 8, Düsseldorf, Germany * E-mail:t.schurmann@icloud.com030320170803307311July 14, 2016Accepted: March 21, March 24, 2017© Copyright 2014 by authors and Scientific Research Publishing Inc. 2014This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/

Simultaneous measurements of position and momentum are considered in n dimensions. We find, that for a particle whose position is strictly localized in a compact domain (spatial uncertainty) with non-empty boundary, the standard deviation of its momentum is sharply bounded by , while is the first Dirichlet eigenvalue of the Laplacian on D.

Uncertainty Principle Dirichlet Eigenvalue Wirtinger Inequality
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Schürmann, T. (2017) The Uncertainty Principle in Terms of Isoperimetric Inequalities. Applied Mathematics, 8, 307-311. https://doi.org/10.4236/am.2017.83025

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