, Volume 41, Issue 9, pp 1415-1436
Date: 26 Feb 2011

Imprints of the Quantum World in Classical Mechanics

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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.

Maurice de Gosson has been financed by the Austrian Research Agency FWF (Projekt “Symplectic Geometry and Applications to TFA and QM”, Projektnummer P20442-N13).