Imprints of the Quantum World in Classical Mechanics
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- de Gosson, M.A. & Hiley, B.J. Found Phys (2011) 41: 1415. doi:10.1007/s10701-011-9544-5
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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.