Experiments with Schr\"odinger Cellular Automata
Quantum Physics
2025-07-23 v2
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.
Cite
@article{arxiv.2406.08586,
title = {Experiments with Schr\"odinger Cellular Automata},
author = {Kees van Berkel and Jan de Graaf and Kees van Hee},
journal= {arXiv preprint arXiv:2406.08586},
year = {2025}
}