A closer look at the uncertainty relation of position and momentum

Abstract

We consider particles prepared by the von Neumann-Lüders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and sufficient condition for finite standard deviations is given. Finally, a new uncertainty relation is derived and it is shown that the latter cannot be improved.

3 pages, introduction shortened, content unchanged

References in corpus (3)

• Formulation of the uncertainty relations in terms of the Renyi entropies
• Identifying wave packet fractional revivals by means of information entropy
• Improved bounds in entropic uncertainty relations

Cited by in corpus (16)

• Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy
• Gravitationally induced uncertainty relations in curved backgrounds
• Uncertainty principle on 3-dimensional manifolds of constant curvature
• Uncertainty Relations for coarse-grained measurements: an overview
• Entropic uncertainty relations and topological-band insulator transitions in 2D gapped Dirac materials
• Relativistic Extended Uncertainty Principle from Spacetime Curvature
• Angular performance measure for tighter uncertainty relations
• On the uncertainty principle in Rindler and Friedmann spacetimes
• On momentum operators given by Killing vectors whose integral curves are geodesics
• The uncertainty principle in terms of isoperimetric inequalities
• On the experimental verification of the uncertainty principle of position and momentum
• Uncertainty relations: curiosities and inconsistencies
• Deterministic Elaboration of Heisenberg's Uncertainty Relation and the Nowhere Differentiability
• Equivalence principle violation from large scale structure
• The Extended Uncertainty Principle from a Projector-Valued Measurement Perspective
• Spontaneous Lorentz symmetry violation from infrared gravity