This Inequality States That for Any Bounded Interval Q=[a,b] and Any Continuously Differentiable f(x)∈C¹(Q) with f(a)=f(b)=0. It Follows That ∫_Q∣f∣² dx≤[(b-a)²/π²] ∫_Q ∣f∣² dx. The Constant (b-a)²/π² Cannot Be Further Improved [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.