峰值量子孤子的广义导引方程：单粒子情形
Generalized guidance equation for peaked quantum solitons: the single particle case
摘要：
我们研究了薛定谔方程的某些非线性推广，该方程在没有外部势作用于粒子的情况下，允许静态孤子2解。我们考虑一类解，它可以表示为线性薛定谔方程的解与峰值量子孤子的乘积，在这个区域中，孤子的大小比线性波的典型变化尺度小得多.在非相对论极限下，孤子服从广义de Broglie-Bohm（dB-B）制导方程。在一级近似下，这个制导方程简化为dB-B制导方程，根据这个方程，它们沿着线性薛定谔波的流体动力流线以所谓的德布罗意-玻姆速度运动。如果我们考虑一个旋量电子的波函数，它的重心将严格按照dB-B制导方程运动。
英文摘要：
We study certain non-linear generalisations of the Schr{ö}dinger equation which admit static solitonic 2 solutions in absence of external potential acting on the particle. We consider a class of solutions that can be written as a product of a solution of the linear Schr{ö}dinger equation with a peaked quantum soliton, in a regime where the size of the soliton is quite smaller than the typical scale of variation of the linear wave. In the non-relativistic limit, the solitons obey a generalized de Broglie-Bohm (dB-B) guidance equation. In first approximation, this guidance equation reduces to the dB-B guidance equation according to which they move at the so-called de Broglie-Bohm velocity along the hydrodynamical flow lines of the linear Schr{ö}dinger wave. If we consider a spinorial electronic wave function a la Dirac, its barycentre is predicted to move exactly in accordance with the dB-B guidance equation.
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