Quantum and Classic Brackets

2000/07/31 by Vladimir V. Kisil
Physics and Astronomy · Mathematics · #math-ph #math.FA #math.MP #math.QA #math.RT #physics.class-ph #quant-ph #msc:81R05 #msc:81P05 #msc:22E70 #msc:43A65

paper · pdf

published as Int. J. Theor. Phys. v.41(2002), no.1, pp.63-77 · LaTeX2e, 16 pages; added subsection with an example

arxiv created 2001/03/22 · arxiv updated 2009/11/30

Abstract

We describe an p-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We do not use any kind of semiclassic approximation or limiting procedures for ℏ → 0. Harmonic oscillator considered within the approach. Keywords: Classic and quantum mechanics, Hamilton and Heisenberg equations, Poisson brackets, commutator, Heisenberg group.

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