KMS Of Academy of mathematics and systems sciences, CAS

Statistics of local value in quantum mechanics | |

Luo, SL | |

2002-09-01 | |

Source Publication | INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS |

ISSN | 0020-7748 |

Volume | 41Issue:9Pages:1713-1731 |

Abstract | Given a quantum mechanical observable and a state, one can construct a classical observable, that is, a real function on the configuration space, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. This optimal estimate turns out to be the quantum mechanical local value, which arises from several contexts such as de Broglie-Bohm's casual approach to quantum mechanics, instantaneous frequency in time frequency analysis, Nelson's quantum fluctuations formalism, and phase-space approach to quantum mechanics. Accordingly, any observable can be decomposed into a local value part and a quantum fluctuation part, which are independent, both geometrically and st |