## 摘要

In classical mechanics, the action and angle variables (J; Θ) can be found by integrating the momentum p with respect to the coordinate q under the constraint of energy conservation. Because it is not known how to extend Riemann integration to operator functions and variables, the classical method of action-angle formalism cannot be extended to quantum mechanics. We show that by using general quantum canonical transformations, one can transform (p; q) into (J; Θ), by which one of the conjugate variables in the Hamiltonian is eliminated. This algebraic integration by quantum canonical transformations gives not only the operator relations between (p; q) and (J; Θ), but also the eigenfunctions of the Hamiltonian and the eigenfunctions of the phase operator. These results offer a new point of view for the action-angle formalism in quantum mechanics.

原文 | ???core.languages.en_GB??? |
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頁（從 - 到） | 555-570 |

頁數 | 16 |

期刊 | Chinese Journal of Physics |

卷 | 49 |

發行號 | 2 |

出版狀態 | 已出版 - 4月 2011 |