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arXiv · 2511.13748

From Newton's equations to the Schr\"odinger equation: domain walls as the quantization condition

Dennis M. Heim
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Abstract

Can particles at definite positions in real space, obeying Newton's equations under an ordinary interaction force, have a coarse-grained description that is the Schr\"odinger equation? We present a medium of companion particles on a line under a force of exactly that kind: each companion pays for the mismatch of the signed inverse gaps to its two neighbors. A binary polarity carried by each companion makes stationary states with nodes dynamically stable and supplies the quantization condition. Finite chains relax into the stationary densities of the box and the harmonic oscillator and develop double-slit fringes. In the smooth limit the Schr\"odinger equation emerges, with $\psi$ carrying two real fields rather than being fundamental.

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Dennis M. Heim. 2025-11-13. From Newton's equations to the Schr\"odinger equation: domain walls as the quantization condition. https://arxiv.org/abs/2511.13748

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