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arXiv · 2406.08586

Experiments with Schr\"odinger Cellular Automata

Kees van Berkel·Jan de Graaf·Kees van Hee
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Abstract

We derive a class of cellular automata for the Schr\"odinger Hamiltonian, including scalar and vector potentials. It is based on a multi-split of the Hamiltonian, resulting in a multi-step unitary evolution operator in discrete time and space. Experiments with one-dimensional automata offer quantitative insight in phase and group velocities, energy levels, related approximation errors, and the evolution of a time-dependent harmonic oscilator. The apparent effects of spatial waveform aliasing are intriguing. Interference experiments with two-dimensional automata include refraction, Davisson-Germer, Mach-Zehnder, single & double slit, and Aharonov-Bohm.

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Kees van Berkel, Jan de Graaf, Kees van Hee. 2024-06-12. Experiments with Schr\"odinger Cellular Automata. https://doi.org/10.22331/q-2025-07-23-1811

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