Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space

Details Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space

2002-10-24

arxiv.org/abs/quant-ph/0210164v2

Physics

Quantum Physics

10 pages, Latex2e file, references added, minor clarifications made

Scientific paper

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Classical mechanics can now be viewed as a deformation of quantum mechanics. The forms of semiquantum approximations to classical mechanics are indicated.

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