Jamet P, Drezet A
Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Neel, F-38000 Grenoble, France.
Chaos. 2021 Oct;31(10):103120. doi: 10.1063/5.0067545.
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 the 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 an atom.
受流体动力学量子力学类似物近期发展的启发[J. W. M. 布什，《流体力学年度评论》47, 269 - 292 (2015)]，我们给出了一个通过完整约束与标量波场耦合的经典粒子的相对论模型。在存在外部库仑场的情况下，我们定义了一个区域，其中粒子以类似于旧的德布罗意相波提议的方式被波引导。此外，这种量子理论的二元力学类似物让人想起1927年德布罗意提出的双解方法，并且能够重现电子在原子中运动的玻尔 - 索末菲半经典量子化公式。
