经典和量子物理中的亥姆霍兹波轨迹
Helmholtz wave trajectories in classical and quantum physics
摘要：
经典和量子波束在静止介质中的行为被证明是由编码在亥姆霍兹方程中的“波势”函数决定的，由光束本身的结构决定，在量子情况下，采取玻姆的“量子势”的形式，因此与其说是“量子”，不如说是“波”的性质。精确的，确定性的运动规律，相互耦合的这一项和描述波状的功能，如衍射和干涉，得到定义良好的哈密顿轨迹方面，并示出减少到通常的几何光学和/或经典动力学的法律时，这个耦合项被忽略。就量子情况而言，本文提出的方法，建议直接扩展的治疗持有经典波，描述了经典的外观，点状粒子的运动，而不诉诸于使用行波包。
英文摘要：
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case, the form of Bohm's "Quantum Potential", which is therefore not so much a "quantum" as a "wave" property. Exact, deterministic motion laws, mutually coupled by this term and describing wave-like features such as diffraction and interference, are obtained in terms of well defined Hamiltonian trajectories, and shown to reduce to the laws of usual geometrical optics and/or classical dynamics when this coupling term is neglected. As far as the quantum case is concerned, the approach proposed in the present paper, suggested by the direct extension of the treatment holding for classical waves, describes the motion of classical-looking, point-like particles, without resorting to the use of travelling wave-packets.
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