To the question of a nonrelativistic wave equation for a system of interacting particles

Details To the question of a nonrelativistic wave equation for a system of interacting particles To the question of a nonrelativistic wave equation for a system of interacting particles

2000-02-02

arxiv.org/abs/quant-ph/0002012v3

Physics

Quantum Physics

17 pages, 3 PostScript figures, RevTeX. This article is a long version of our article in Phys. Rev. A 61, 014101 (2000)

Scientific paper

10.1103/PhysRevA.61.014101

It is shown that the Schr\"{o}dinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation velocity. For a system of interacting particles, a fully nonrelativistic nonlinear system of integro-differential equations is proposed. In the case where the size of the system of particles is of the same order as the Compton wavelength associated with particles, certain essential differences are shown to exist as compared with traditional consequences of the nonrelativistic Schr\"{o}dinger equation.

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