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A Closer Look at the Uncertainty Relation of Position and Momentum

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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 Δx≥π ℏ is derived and it is shown that this bound cannot be improved.

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Authors and Affiliations

  1. Jülich Supercomputing Centre, Jülich Research Centre, 52425, Jülich, Germany

    Thomas Schürmann & Ingo Hoffmann

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  1. Thomas Schürmann
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  2. Ingo Hoffmann
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Correspondence to Thomas Schürmann.

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Schürmann, T., Hoffmann, I. A Closer Look at the Uncertainty Relation of Position and Momentum. Found Phys 39, 958–963 (2009). https://doi.org/10.1007/s10701-009-9310-0

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  • DOI: https://doi.org/10.1007/s10701-009-9310-0

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