TITLE:
The Uncertainty Principle in Terms of Isoperimetric Inequalities
AUTHORS:
Thomas Schürmann
KEYWORDS:
Uncertainty Principle, Dirichlet Eigenvalue, Wirtinger Inequality
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.3,
March
24,
2017
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 (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.