## 摘要

The current trajectory interpretation of quantum mechanics is based on an ensemble viewpoint that the evolution of an ensemble of Bohmian trajectories guided by the same wavefunction Ψ converges asymptotically to the quantum probability |Ψ|2. Instead of the Bohm's ensemble-trajectory interpretation, the present paper gives a single-trajectory interpretation of quantum mechanics by showing that the distribution of a single chaotic complex-valued trajectory is enough to synthesize the quantum probability. A chaotic complex-valued trajectory manifests both space-filling (ergodic) and ensemble features. The space-filling feature endows a chaotic trajectory with an invariant statistical distribution, while the ensemble feature enables a complex-valued trajectory to envelop the motion of an ensemble of real trajectories. The comparison between complex-valued and real-valued Bohmian trajectories shows that without the participation of its imaginary part, a single real-valued trajectory loses the ensemble information contained in the wavefunction Ψ, and this explains the reason why we have to employ an ensemble of real-valued Bohmian trajectories to recover the quantum probability |Ψ|2.

原文 | English |
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頁（從 - 到） | 428-437 |

頁數 | 10 |

期刊 | International Journal of Quantum Chemistry |

卷 | 116 |

發行號 | 6 |

DOIs | |

出版狀態 | Published - 2016 3月 15 |

## All Science Journal Classification (ASJC) codes

- 原子與分子物理與光學
- 凝聚態物理學
- 物理與理論化學