电动粒子的Doebner-Goldin方程隐含的应用
Doebner-Goldin Equation for Electrodynamic Particle. The Implied Applications
摘要：
本文建立了电磁波的麦克斯韦方程组和相应的经典波动方程组，该电磁波的发生源是一个静止质量为零的运动振荡电荷，它包括一个在通常的保守势和附加摩擦力$f$的力场中运动的粒子。在德布罗意波长尺度和经典速度极限下，全波方程分解为描述粒子动力学运动的分量方程，对于$f=0$，该分量方程与前面提到的通常的线性薛定谔方程相同。依赖于$f$的概率密度通常表示一个具有实扩散常数的可观测扩散电流;这和粒子通常的量子扩散电流作为一个整体在绝热条件下是守恒的，并且服从福克-普朗克方程。哈密顿算符中相应的额外的、依赖于$f$的项与H. D. Doebner和G.A.戈尔丁摩擦产生的粒子的波振幅的阻尼，可以很好地描述由于辐射（去）极化场，这总是由粒子的振荡电荷在（非极性）电介质中产生的效果。电介质真空中的辐射退极化场有两种不同的意义：它参与对另一个粒子施加一种吸引的、退极化的辐射力，这种辐射力在总体上类似于我们前面提到的牛顿万有引力;它对粒子本身施加一种吸引的、自退极化的辐射力，这种辐射力的时间速率直接给出摩擦力$f$。
英文摘要：
We set up the Maxwell's equations and the corresponding classical wave equations for the electromagnetic waves which together with the generating source, a traveling oscillatory charge of zero rest mass, comprise a particle traveling in the force field of an usual conservative potential and an additional frictional force $f$. At the de Broglie wavelength scale and in the classic-velocity limit, the total wave equation decomposes into a component equation describing the particle kinetic motion, which for $f=0$ identifies with the usual linear Schrödinger equation as previously. The $f$-dependent probability density presents generally an observable diffusion current of a real diffusion constant; this and the particle's usual quantum diffusion current as a whole are under adiabatic condition conserved and obey the Fokker-Planck equation. The corresponding extra, $f$-dependent term in the Hamiltonian operator identifies with that obtained by H.-D. Doebner and G.A. Goldin. The friction produces to the particle's wave amplitude a damping that can describe well the effect due to a radiation (de)polarization field, which is always by-produced by the particle's oscillatory charge in a (nonpolar) dielectric medium. The radiation depolarization field in a dielectric vacuum has two separate significances: it participates to exert on another particle an attractive, depolarization radiation force which resembles in overall respects Newton's universal gravity as we showed earlier, and it exerts on the particle itself an attractive, self depolarization radiation force whose time rate gives directly the frictional force $f$.
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