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Hamiltonian formulation of generalized quantum dynamics

Quantum mechanical problem

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Abstract

The Hamiltonian formulation of the usual complex quantum mechanics in the theory of generalized quantum dynamics is discussed. After the total trace Lagrangian, total trace Hamiltonian and two kinds of Poisson brackets are introduced, both the equations of motion of some total trace functionals which are expressed by total trace Poisson brackets and the equations of motion of some operators which are expressed by the without-total-trace Poisson brackets are obtained. Then a set of basic equations of motion of the usual complex quantum mechanics are obtained, which are also expressed by the Poisson brackets and total trace Hamiltonian in the generalized quantum dynamics. The set of equations of motion are consistent with the corresponding Heisenberg equations.

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References

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Authors and Affiliations

  1. CCAST (World Lab), 100080, Beijing, China

    Ning Wu & Tunan Ruan

  2. Department of Physics, University of Science and Technology of China, 230026, Hefei, China

    Ning Wu & Tunan Ruan

Authors
  1. Ning Wu
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  2. Tunan Ruan
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Additional information

Project supported by Prof. T.D. Lee’s NNSC Grant, the National Natural Science Foundation of China, the Foundation of Ph. D. Directing Programme of Chinese University, and the Chinese Academy of Sciences.

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Wu, N., Ruan, T. Hamiltonian formulation of generalized quantum dynamics. Sci. China Ser. A-Math. 40, 417–421 (1997). https://doi.org/10.1007/BF02911443

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  • DOI: https://doi.org/10.1007/BF02911443

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