The uncertainty principle in terms of isoperimetric inequalities

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 ${\sigma }_p\ge {\lambda }_1^{1/2}\hslash$, while ${\lambda }_1$ is the first Dirichlet eigenvalue of the Laplacian on $D$.

2 pages

References in corpus (1)

• A closer look at the uncertainty relation of position and momentum

Cited by in corpus (2)

• Uncertainty principle on 3-dimensional manifolds of constant curvature
• Uncertainty relations: curiosities and inconsistencies