Krahn, E. (1926) über Minimaleigenschaften der Kugel in drei und mehr Dimensionen. Acta Comm. Univ. Tartu (Dorpat), A9, 1. [English Translation: Lumiste, ü. and Peetre, J., Eds., Edgar Krahn, 1894-1961, A Centenary Volume, IOS Press, Amsterdam, 1994, Chapter 6.]

has been cited by the following article:

• 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.