1. A mechanical analog of Bohr's atom based on de Broglie's double-solution approach
- Author
-
Pierre Jamet, Aurélien Drezet, Institut Néel (NEEL), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)
- Subjects
electron ,particle ,semiclassical ,Field (physics) ,General Physics and Astronomy ,Semiclassical physics ,Electron ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Quantization (physics) ,[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] ,Quantum mechanics ,0103 physical sciences ,010306 general physics ,Quantum ,Mathematical Physics ,fluid ,Physics ,Quantum Physics ,model ,atom ,Applied Mathematics ,quantum mechanics ,Statistical and Nonlinear Physics ,Bohr model ,relativistic ,hydrodynamics ,symbols ,duality ,Coulomb ,quantization ,Matter wave ,classical ,Scalar field - 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., Comment: 15 pages
- Published
- 2021