2024/06/12 by van Berkel, Kees, de Graaf, Jan, van Hee, Kees
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2406.08586
We derive a class of cellular automata for the Schrödinger 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.