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Foundations of Physics

, Volume 39, Issue 8, pp 958–963 | Cite as

A Closer Look at the Uncertainty Relation of Position and Momentum

  • Thomas Schürmann
  • Ingo Hoffmann
Article

Abstract

We consider particles prepared by a single slit diffraction experiment. For those particles the standard deviation σ p of the momentum is discussed. We find out that σ p =∞ is not an exception but a rather typical case. A necessary and sufficient condition for σ p <∞ is given. Finally, the inequality σ p Δxπ is derived and it is shown that this bound cannot be improved.

Keywords

Uncertainty relation Quantum measurement process Wirtinger inequality 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Jülich Supercomputing CentreJülich Research CentreJülichGermany

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