Unfinished history and paradoxes of quantum potential. I. Non-relativistic origin, history and paradoxes

E.A. Tagirov1

Abstract

This is the first of two related papers analyzing and explaining the origin, manifestations and parodoxical features of the quantum potential (QP) from the non-relativistic and relativistic points of view. The QP arises in the quantum Hamiltonian under various procedures of quantization of natural systems, i.e., those whose Hamilton functions are positive-definite quadratic forms in momenta with coefficients depending on the coordinates in (n-dimensional) configurational space Vn thus endowed with a Riemannian structure. The result of quantization may be considered as quantum mechanics (QM) of a particle in Vn in the normal Gaussian coordinate system in the globally static space-time V1,n. Contradiction of the QP to the General Covariance and Equivalence principles is discussed.

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