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Random walk as a model of motion in a quantum harmonic oscillator

Volume 49 / 2022

Zbigniew S. Kowalski Applicationes Mathematicae 49 (2022), 185-195 MSC: Primary 81S99; Secondary 37A05, 65L10. DOI: 10.4064/am2447-12-2022 Published online: 4 January 2023


The one-dimensional quantum harmonic oscillator is considered. The wave solution of the Schrödinger equation determines the model of motion of particles in the $n$-quantum state as orbits of a stationary random walk at the moment of jump from the $n-1$-quantum to the $n$-quantum state. Numerical solutions are given for $n=2,3.$


  • Zbigniew S. KowalskiFaculty of Pure and Applied Mathematics
    Wrocław University of Science and Technology
    50-370 Wrocław, Poland
    ORCID: 0000-0001-6220-2562

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