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

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 ${\sigma }_p\Delta x\ge \pi \hslash$. 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 Fernández-Guasti (2022) [9].

7 pages, 4 figures

References in corpus (2)

• Heisenberg's Uncertainty Principle
• On the uncertainty principle in Rindler and Friedmann spacetimes

Cited by in corpus (1)

• The Extended Uncertainty Principle from a Projector-Valued Measurement Perspective