• DOI:10.1088/0305-4470/36/23/101
• Corpus ID: 15505801

Quantum mechanics as an approximation to classical mechanics in Hilbert space

@article{Bracken2002QuantumMA,
  title={Quantum mechanics as an approximation to classical mechanics in Hilbert space},
  author={A. Bracken},
  journal={Journal of Physics A},
  year={2002},
  volume={36},
  url={https://api.semanticscholar.org/CorpusID:15505801}
}

• A. Bracken
• Published 24 October 2002
• Physics
• Journal of Physics A

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms… 

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.