Foundations of Physics

, Volume 41, Issue 9, pp 1415–1436

Imprints of the Quantum World in Classical Mechanics

Article

Abstract

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity of discussing the group of Hamiltonian canonical transformations which is a non-linear variant of the usual symplectic group.

Keywords

Quantization Schrödinger’s equation Hamiltonian flows Symplectic covariance of Weyl calculus Stone’s theorem 

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.NuHAG, Fakultät für MathematikUniversität WienWienAustria
  2. 2.TPRU, BirkbeckUniversity of LondonLondonUK

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