Optimal guidance law in quantum mechanics

Ciann-Dong Yang, Lieh Lieh Cheng, Ming Hsien Hsia

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Following the de Broglie's idea of pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle's motion is just the wavefunction ψ(t,x), a solution to Schrödinger equation. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function ψψ.

Original languageEnglish
Title of host publication26th Chinese Control and Decision Conference, CCDC 2014
PublisherIEEE Computer Society
Pages1095-1100
Number of pages6
ISBN (Print)9781479937066
DOIs
Publication statusPublished - 2014 Jan 1
Event26th Chinese Control and Decision Conference, CCDC 2014 - Changsha, China
Duration: 2014 May 312014 Jun 2

Publication series

Name26th Chinese Control and Decision Conference, CCDC 2014

Other

Other26th Chinese Control and Decision Conference, CCDC 2014
CountryChina
CityChangsha
Period14-05-3114-06-02

All Science Journal Classification (ASJC) codes

  • Information Systems and Management
  • Control and Systems Engineering

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  • Cite this

    Yang, C-D., Cheng, L. L., & Hsia, M. H. (2014). Optimal guidance law in quantum mechanics. In 26th Chinese Control and Decision Conference, CCDC 2014 (pp. 1095-1100). [6852328] (26th Chinese Control and Decision Conference, CCDC 2014). IEEE Computer Society. https://doi.org/10.1109/CCDC.2014.6852328