Abstract
The author has recently proposed a “quasi-classical” theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field χ(x, t), interacting with each other via nonlinearity in the equation of motion for χ. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from χ a configuration-space wave function Ψ(x 1,x 2,t), and that the theory requires that Ψ satisfy the two-particle Schrödinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schrödinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a “crutch” theory which has subsequently to be “quantized.” The quasi-classical theory also suggests the existence of a preferred “absolute” gauge for the electromagnetic potentials.
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Wignall, J.W.G. The nonrelativistic Schrödinger equation in “quasi-classical” theory. Found Phys 17, 123–147 (1987). https://doi.org/10.1007/BF00733204
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DOI: https://doi.org/10.1007/BF00733204