From Double-Slit Interference to a Galton-Board Analogy for Quantum Tunnelling: An Experimental and Computational Study

This preprint presents an experimental and computational study of double-slit interference, probability modelling, and a deliberately limited Galton-board analogy for quantum tunnelling. A red-laser double-slit experiment was performed using slit separations of 0.20, 0.30, and 0.45 mm. Direct fringe-spacing analysis gave wavelength estimates of 680.01–713.94 nm, while FFT-based analysis gave 679.99–715.72 nm. A 15-layer Galton board was then investigated experimentally and numerically. Three physical trials showed a broader and slightly biased distribution compared with an ideal symmetric binomial model, with p≈0.55 providing the closest fit among the tested values. Monte Carlo simulations were used to examine the effects of layer number n and branching probability p. Finally, a mathematical mapping was defined between the Galton-board probability model and the exponential form of an idealised tunnelling transmission coefficient. In this mapping, n controls an equivalent barrier width and p controls an equivalent decay constant and barrier-energy difference. These quantities are pedagogical equivalents only: the Galton board is a classical stochastic system and does not reproduce wavefunction phase, coherent superposition, or genuine quantum tunnelling. This work is a non-peer-reviewed preprint of a student research project.