Imprints of the Quantum World in Classical Mechanics

Foundations of Physics 41 (9):1415-1436 (2011)

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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DOI 10.1007/s10701-011-9544-5
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Why the Hamilton Operator Alone Is Not Enough.I. Schmelzer - 2009 - Foundations of Physics 39 (5):486-498.
Pure Quantum Interpretations Are Not Viable.I. Schmelzer - 2011 - Foundations of Physics 41 (2):159-177.

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