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Title: A quasi-Bohmian approach for a homogeneous spherical solid body based on its geometric structure

In this paper we express the space of rotation as a Riemannian space and try to generalize the classical equations of motion of a homogeneous spherical solid body in the domain of quantum mechanics. This is done within Bohm's view of quantum mechanics, but we do not use the Schrödinger equation. Instead, we assume that in addition to the classical potential there is an extra potential and try to obtain it. In doing this, we start from a classical picture based on Hamilton-Jacobi formalism and statistical mechanics but we use an interpretation which is different from the classical one. Then, we introduce a proper action and extremize it. This procedure gives us a mathematical identity for the extra potential that limits its form. The classical mechanics is a trivial solution of this method. In the simplest cases where the extra potential is not a constant, a mathematical identity determines it uniquely. In fact the first nontrivial potential, apart from some constant coefficients which are determined by experiment, is the usual Bohmian quantum potential.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Department of Physics, Shahid Beheshti University, G. C., Evin, Tehran 19839 (Iran, Islamic Republic of)
  2. (IPM), Tehran (Iran, Islamic Republic of)
  3. Institutes for Theoretical Physics and Mathematics (IPM), Tehran (Iran, Islamic Republic of)
  4. (Iran, Islamic Republic of)
Publication Date:
OSTI Identifier:
22217737
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLASSICAL MECHANICS; EQUATIONS OF MOTION; HAMILTON-JACOBI EQUATIONS; QUANTUM MECHANICS; RIEMANN SPACE; SPHERICAL CONFIGURATION; STATISTICAL MECHANICS