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arXiv · 2211.14724

On the experimental verification of the uncertainty principle of position and momentum

Thomas Schürmann·Ingo Hoffmann·Winfrid Görlich
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Abstract

Historically, Kennard was the first to choose the standard deviation as a quantitative measure of uncertainty, and neither he nor Heisenberg explicitly explained why this choice should be appropriate from the experimental physical point of view. If a particle is prepared by a single slit of spatial width $\Delta x$, it has been shown that a finite standard deviation $\sigma_p<\infty$ can only be ensured if the wave-function is zero at the edge of $\Delta x$, otherwise it does not exist [8]. Under this circumstances the corresponding sharp inequality is $\sigma_p \Delta x\geq \pi\hbar$. This bound will be reconsidered from the mathematical point of view in terms of a variational problem in Hilbert space and will furthermore be tested in a 4f-single slit diffraction experiment of a laser beam. Our results will be compared with a laser-experiment recently given by Fern\'andez-Guasti (2022) [9].

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Thomas Schürmann, Ingo Hoffmann, Winfrid Görlich. 2022-11-27. On the experimental verification of the uncertainty principle of position and momentum. https://doi.org/10.1016/j.physleta.2023.128787

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