Hamiltonian Structure of the Schrödinger Classical Dynamical System

Massimo Tessarotto, Michael Mond, Davide Batic

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

The connection between quantum mechanics and classical statistical mechanics has motivated in the past the representation of the Schrödinger quantum-wave equation in terms of “projections” onto the quantum configuration space of suitable phase-space asymptotic kinetic models. This feature has suggested the search of a possible exact super-dimensional classical dynamical system (CDS), denoted as Schrödinger CDS, which uniquely determines the time-evolution of the underlying quantum state describing a set of N like and mutually interacting quantum particles. In this paper the realization of the same CDS in terms of a coupled set of Hamiltonian systems is established. These are respectively associated with a quantum-hydrodynamic CDS advancing in time the quantum fluid velocity and a further one the RD-CDS, describing the relative dynamics with respect to the quantum fluid.

Original languageEnglish
Pages (from-to)1127-1167
Number of pages41
JournalFoundations of Physics
Volume46
Issue number9
DOIs
StatePublished - 1 Sep 2016

Keywords

  • Classical dynamical systems
  • Inverse kinetic and statistical descriptions
  • Nonlocality
  • Quantum hydrodynamic equations
  • Time-dependent Schrödinger equation

ASJC Scopus subject areas

  • General Physics and Astronomy

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