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  The connection between bohmian mechanics and many-particle quantum hydrodynamics

Renziehausen, K., & Barth, I. (2020). The connection between bohmian mechanics and many-particle quantum hydrodynamics. Foundations of Physics Letters, 50(8), 772-798. doi:10.1007/s10701-020-00349-1.

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s10701-020-00349-1 (Publisher version), 274KB
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https://doi.org/10.1007/s10701-020-00349-1 (Publisher version)
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Renziehausen, Klaus1, Author              
Barth, Ingo1, Author              
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1Max Planck Institute of Microstructure Physics, Max Planck Society, Weinberg 2, 06120 Halle, DE, ou_2415691              

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 Abstract: Bohm developed the Bohmian mechanics (BM), in which the Schrödinger 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 in 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.

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 Dates: 2020-06-252020-08
 Publication Status: Published in print
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 Identifiers: BibTex Citekey: P13954
DOI: 10.1007/s10701-020-00349-1
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Title: Foundations of Physics Letters
  Other : Found. Phys. Lett.
Source Genre: Journal
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Publ. Info: New York : Plenum Press
Pages: - Volume / Issue: 50 (8) Sequence Number: - Start / End Page: 772 - 798 Identifier: ISSN: 0894-9875
CoNE: https://pure.mpg.de/cone/journals/resource/954925264200