Foundations of Physics

, Volume 41, Issue 9, pp 1415-1436

First online:

Imprints of the Quantum World in Classical Mechanics

  • Maurice A. de GossonAffiliated withNuHAG, Fakultät für Mathematik, Universität Wien Email author 
  • , Basil J. HileyAffiliated withTPRU, Birkbeck, University of London

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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