Bohm developed the Bohmian mechanics (BM), in which the Schr\"odinger equation is transformed into two differential equations: A continuity equation and an equation of motion similar to the Newtonian equation of motion. This transformation can be executed both for single-particle systems and for many-particle systems. Later, Kuzmenkov and Maksimov used basic quantum mechanics for the derivation of many-particle quantum hydrodynamics (MPQHD) including one differential equation for the mass balance and two differential equations for the momentum balance, and we extended their analysis in a prework [K. Renziehausen, I. Barth, Prog. Theor. Exp. Phys. 2018, 013A05 (2018)] for the case that the particle ensemble consists of different particle sorts. The purpose of this paper is to show how the differential equations of MPQHD can be derived for such a particle ensemble with the differential equations of BM as a starting point. Moreover, our discussion clarifies that the differential equations of MPQHD are more suitable for an analysis of many-particle systems than the differential equations of BM because the differential equations of MPQHD depend on a single position vector only while the differential equations of BM depend on the complete set of all particle coordinates.

中文翻译：

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玻姆力学与多粒子量子流体动力学之间的联系

本文的目的是展示如何以 BM 的微分方程为起点，为这种粒子系综推导出 MPQHD 的微分方程。此外，我们的讨论阐明了 MPQHD 的微分方程比 BM 的微分方程更适合分析多粒子系统，因为 MPQHD 的微分方程仅依赖于单个位置向量，而 BM 的微分方程依赖于所有粒子坐标的完整集合。