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Experimental verification of the Heisenberg Uncertainty Principle via Single-Slit Diffraction

Evan Zhang

Published Mar 24, 2026• 0 citations

Abstract

This experiment investigates the Heisenberg Uncertainty Principle (HUP) through an optical analogue using Single-slit diffraction of a monochromatic He–Ne laser. The spatial confinement of light through slits of varying width is compared with the resulting diffraction patterns, providing a means to examine the relationship between position uncertainty ∆x and transverse momentum uncertainty ∆px. Diffraction patterns were recorded using a photodiode detector, and the angular positions of the first minima were determined and used to estimate the spread in momentum via the de-Broglie relation. The results demonstrates and are consistent with the expected inverse relationship. The measured diffraction patterns were also found to adhere to the Fraunhofer diffraction relation, supporting the validity of the experimental model and the goodness of fit of the data.The calculated uncertainty products were further found to be consistent with the expected magnitude of Planck's constant. and therefore the the findings support the interpretation of diffraction as a classifcal manifestation of the Foruier relation between position and momentum space. Thus providing a physically intuituve demonstration of Heisenberg's Uncertainty Principle.

DOI: 10.5281/zenodo.19202403

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We show that the quantum mechanical interpretation of the diffraction of light on a slit, when a wave function is assigned to a photon, can be used for a direct experimental study of Heisenberg’s position-momentum and equivalent positionwave vector uncertainty relation for the photon. Results of an experimental test of the position-wave vector uncertainty relation, where the wavelength is used as the input parameter, are given and they very well confirm our approach. The same experimental results can also be used for a test of the position-momentum uncertainty relation when the momentum p0 of a photon is known as the input parameter. We show that a measurement of p0, independent of the knowledge of the value of the Planck’s constant, is possible. Using that value of p0, a test of the position-momentum uncertainty relation could be regarded as a method for a direct measurement of the Planck’s constant. This is discussed, since the diffraction pattern is also well described by classical electrodynamics in the considered experimental conditions. This approach for testing the Heisenberg’s uncertainty relations is very simple and consequently suitable as a quantitative exercise in undergraduate experimental courses, as well as a visual and attractive demonstration of the Heisenberg’s uncertainty principle in courses of quantum mechanics.

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We described a simple idea for experimental verification of the uncertainty principle for light waves. We used a single-slit diffraction of a laser beam for measuring the angular width of zero-order diffraction maximum and obtained the corresponding wave number uncertainty. We will assume that the uncertainty in position is the slit width. For the acquisition of the experimental data and their further analysis, we used a computer. Because of its simplicity this experiment is very suitable for demonstration, as well as for a quantitative exercise at universities and final year of high school studies.

Heisenberg's uncertainty principle explains single slit diffraction1 where maximum is always at the centre. The same experiment has been conducted but with transparent walls i.e. the material present on either side of the slit, instead of opaque material. The observed result is a minimum at the centre in between two maximum. It is intuitive that atleast some photons passed through the slit must end up at the centre of the diffraction pattern but the result is different. The diffraction pattern occurs as the photons interact with the material around the slit. While uncertainty principle cannot give quantitative explanation as the photons confined in gap between slits still occupy the same space whether it is passing through a slit or not. This paper discusses various experiments and results by examining the interactions between photons and the material of the wall which makes the slit for better understanding of properties of light.

The exact analytical values of the position and momentum information entropies are calculated for the single-slit and double-slit diffraction experiments. In both cases, the product of the exponentials of the entropies is strictly greater than the lower bound $\ensuremath{\pi}e\ensuremath{\Elzxh}$ given by the optimal entropic uncertainty relation for position and momentum, which implies that the single-slit and double-slit configurations are not minimum-uncertainty states. The results obtained show that the position-momentum entropic uncertainty relation provides a rigorous quantitative expression for the uncertainty principle in these experiments, unlike the Heisenberg inequality for standard deviations. However, it is also shown that, in the double-slit experiment, wave-particle duality cannot be derived from the entropic uncertainty relation.