### Abstract

For an intrinsic quantum uncertainty described by |x - x(t)| ≤ Δx and |p - p(t)|≤ Δp, with ΔxΔp ≥ h/2, we establish a state-space model governed by the quantum Hamilton equations q = f(q, p) and p == g(q, p) such that their solutions (q(t), p(t)) satisfy the given uncertainty bound and meanwhile, the statistical distributions of the trajectory sets {q(t)} and {p(t)} exactly reproduce the probability density functions ψ (x)ψ(x) and ψ (p)ψ(p) prescribed a priori. Although actual quantum trajectories are random and non-differentiable, we point out that a complex trajectory q(t) solved from the state-space model provides an uncertainty boundary encompassing an ensemble of quantum trajectories in such a way that its real part q_{R} (t) provides the mean trajectory, while its imaginary part q_{1} (t) gives the radius of deviation of the quantum trajectories from the mean traj ectory.

Original language | English |
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Title of host publication | 2013 10th IEEE International Conference on Control and Automation, ICCA 2013 |

Pages | 1766-1771 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2013 Aug 26 |

Event | 2013 10th IEEE International Conference on Control and Automation, ICCA 2013 - Hangzhou, China Duration: 2013 Jun 12 → 2013 Jun 14 |

### Publication series

Name | IEEE International Conference on Control and Automation, ICCA |
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ISSN (Print) | 1948-3449 |

ISSN (Electronic) | 1948-3457 |

### Other

Other | 2013 10th IEEE International Conference on Control and Automation, ICCA 2013 |
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Country | China |

City | Hangzhou |

Period | 13-06-12 → 13-06-14 |

### All Science Journal Classification (ASJC) codes

- Artificial Intelligence
- Computer Science Applications
- Control and Systems Engineering
- Electrical and Electronic Engineering
- Industrial and Manufacturing Engineering

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## Cite this

*2013 10th IEEE International Conference on Control and Automation, ICCA 2013*(pp. 1766-1771). [6564959] (IEEE International Conference on Control and Automation, ICCA). https://doi.org/10.1109/ICCA.2013.6564959