Foundations of Physics

, Volume 41, Issue 9, pp 1415–1436

Imprints of the Quantum World in Classical Mechanics


DOI: 10.1007/s10701-011-9544-5

Cite this article as:
de Gosson, M.A. & Hiley, B.J. Found Phys (2011) 41: 1415. doi:10.1007/s10701-011-9544-5


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.


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

Copyright information

© 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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