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arXiv · 1606.07936

The uncertainty principle in terms of isoperimetric inequalities

Thomas Schürmann
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Abstract

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 $D\subset \mathbb{R}^n$ (spatial uncertainty) with non-empty boundary, the standard deviation of its momentum is sharply bounded by $σ_p \geq λ_1^{1/2}\hbar$, while $λ_1$ is the first Dirichlet eigenvalue of the Laplacian on $D$.

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Thomas Schürmann. 2016-06-25. The uncertainty principle in terms of isoperimetric inequalities. https://doi.org/10.4236/am.2017.83025

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