Bohm Trajectories for a Particle in a Two-Dimensional Circular Billiard

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This Demonstration considers two trajectories of a quantum particle in a two-dimensional configuration space in which the particle is trapped in a "circular billiard potential" [1]. The trajectories of the particle can then exhibit a rich dynamical structure. The motion ranges from periodic to quasi-periodic to fully chaotic. In the de Broglie–Bohm (or causal) interpretation of quantum mechanics [2, 3], the particle position and momentum are well defined, and the motion can be described by continuous evolution according to the time-dependent Schrödinger equation. The nodal point near the circular origin and the wave density restrict the motion of the particle to a region around the center of the billiard.
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Contributed by: Klaus von Bloh (August 2017)
After work by: O. F. de Alcantara Bonfim, J. Florencio and F. C. Sá Barreto
Open content licensed under CC BY-NC-SA
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The results will be more accurate by increasing PlotPoints, AccuracyGoal, PrecisionGoal and MaxSteps in the code.
References
[1] O. F. de Alcantara Bonfim, J. Florencio and F.C. Sá Barreto, "Chaotic Bohm’s Trajectories in a Quantum Circular Billiard," Physics Letters A, 277(3), 2000 pp. 129–134. doi:10.1016/S0375-9601(00)00705-2.
[2] "Bohmian-Mechanics.net." (Jul 28, 2017) www.bohmian-mechanics.net/index.html.
[3] S. Goldstein. "Bohmian Mechanics." The Stanford Encyclopedia of Philosophy. (Jul 28, 2017)plato.stanford.edu/entries/qm-bohm.