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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Elastic scattering in stochastic mechanics

Maurizio Serva

Published Oct 1, 1984• 4 citations
Publisher
DOI
10.1007/bf02747274

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•Dec 21, 2020•0 citations
Codebase for investigating a model in which quantum mechanics emerges from classical elastic scattering in an amorphous medium. Three sectors, each with independent tests: Sector 1 (Foam): DEC Bloch analysis on periodic foam complexes (C15, Weaire-Phelan, Kelvin, FCC). C15 Laves phase: delta_v/v = 0.93%, compatible with cavity Lorentz bounds (10^-18) with 27x margin. GRB dispersion n=2 from symmetry. Gauge-elastic bridge r ~ 1.0. 370 tests. Sector 2 (Particles): Topological defects (disclination loops) in medium with cubic O_h order. Spinorial sectors (720 deg) from binary octahedral group 2O without postulating SU(2). Hopping coupling, mode constraints, worldline parity on C15. 130+ tests. Sector 3 (Bombardment): QLM scattering -> gamma = kappa c/R -> D = hbar/(2m) -> Schrodinger equation (Madelung transform). Transport cross-section Sigma_tr measured via FDTD. Elastic scattering resolves Le Sage heating. ~30 tests. Total: 500+ tests, Python 3.9 / NumPy / SciPy.
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach to solving the problem of scattering of elementary particles on crystals can serve as an alternative to the Louis de Broglie hypothesis about the wave properties of material particles. The results of calculations by formula (2.2), presented in this pa-per, are in good agreement with the experimentally obtained electron diffraction patterns and X-ray diffraction patterns and the Davisson-Germer experiments.
In this note, we try to develop bound state quantum mechanics directly from statistical arguments. The key idea, we argue, is that a statistical treatment of a system considers “free particles” together with a stochastic equilibrium driving mechanism. If an acceleration driving potential exists (as in classical statistical mechanics), it alters the results, but does not change the main scenario of free particles interacting through a stochastic mechanism at a point because one does not follow particles in time, noting how they accelerate as they travel. (For example, a Maxwell-Boltzmann gas distribution is based on two body elastic scattering whether there is a potential or not. The potential affects the density, but not the relative momentum probabilities at any x.) For the quantum case, the potential V(x) is the stochastic equilibrium driver, but on average kinetic energy plus potential must equal total energy. Again, one does not follow the quantum particle in time trying to see if or how it accelerates.