On the experimental verification of the uncertainty principle of position and momentum
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 $Δx$, it has been shown that a finite standard deviation $σ_p<\infty$ can only be ensured if the wave-function is zero at the edge of $Δx$, otherwise it does not exist [8]. Under this circumstances the corresponding sharp inequality is $σ_p Δx\geq π\hbar$. 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 Fernández-Guasti (2022) [9].