Equivalent Quantum Equations in a System Inspired by Bouncing Droplets Experiments
Equivalent Quantum Equations in a System Inspired by Bouncing Droplets Experiments
复制标题
受弹跳液滴实验启发的系统中的等效量子方程
DOI：
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发表时间：
2016
影响因子：
1.5
通讯作者：
Christian Borghesi
中科院分区：
文献类型：
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作者：
Christian Borghesi
本文研究了一个由携带横波的弹性介质和一个点状高弹性介质密度（称为固结）组成的经典理论体系。我们计算了固结的运动方程以及该系统的波动方程。之后我们总是考虑固结不再是波源的情况。然后固结服从一般的协变制导公式，使得低速近似于等效的德布罗意-玻姆制导公式。凝固运动时，就好像存在一个等效的量子势。检索了严格等效的自由Schrödinger方程，以及线性或球形腔中的量子定态。我们计算混凝土的能量（和动量），自然地由振动弹性介质的能量（和动量）密度定义。如果满足关于振荡振幅的一个条件，就会令人惊奇地发现，凝结体的能量和动量不仅可以用量子力学的相同形式来表示，而且还可以用等价的相对论公式来表示。
In this paper we study a classical and theoretical system which consists of an elastic medium carrying transverse waves and one point-like high elastic medium density, called concretion. We compute the equation of motion for the concretion as well as the wave equation of this system. Afterwards we always consider the case where the concretion is not the wave source any longer. Then the concretion obeys a general and covariant guidance formula, which leads in low-velocity approximation to an equivalent de Broglie-Bohm guidance formula. The concretion moves then as if exists an equivalent quantum potential. A strictly equivalent free Schrödinger equation is retrieved, as well as the quantum stationary states in a linear or spherical cavity. We compute the energy (and momentum) of the concretion, naturally defined from the energy (and momentum) density of the vibrating elastic medium. Provided one condition about the amplitude of oscillation is fulfilled, it strikingly appears that the energy and momentum of the concretion not only are written in the same form as in quantum mechanics, but also encapsulate equivalent relativistic formulas.