The Uncertainty Principle in Terms of Isoperimetric Inequalities

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DOI: 10.4236/am.2017.83025    397 Downloads   489 Views  


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.

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


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