A mechanical analog of Bohr's atom based on de Broglie's double-solution approach

• URL: http://arxiv.org/abs/2106.08997v2
• Date: Wed, 27 Oct 2021 11:32:44 GMT
• Title: A mechanical analog of Bohr's atom based on de Broglie's double-solution approach
• Authors: Pierre Jamet and Aur\'elien Drezet
• Abstract summary: We provide a relativistic model for a classical particle coupled to a scalar wave-field through a holonomic constraint. This dualistic mechanical analog of the quantum theory is reminiscent of the double-solution approach suggested by de Broglie in 1927.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Motivated by recent developments of hydrodynamical quantum mechanical analogs [J. W. M. Bush, Annu. Rev. Fluid Mech. 47, 269-292 (2015)] we provide a relativistic model for a classical particle coupled to a scalar wave-field through a holonomic constraint. In presence of an external Coulomb field we define a regime where the particle is guided by the wave in a way similar to the old de Broglie phase-wave proposal. Moreover, this dualistic mechanical analog of the quantum theory is reminiscent of the double-solution approach suggested by de Broglie in 1927 and is able to reproduce the Bohr-Sommerfeld semiclassical quantization formula for an electron moving in a atom.

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