Optimal Guidance Law in Quantum Mechanics
Following the de Broglies 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 particles motion is just the wavefunction Ψ(t,x),a solution to Schr(o)dinger 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 Ψ*Ψ.
Stochastic Control Optimal Guidance Quantum Trajectory Pilot Wave
Ciann-Dong Yang Lieh-Lieh Cheng Ming-Hsien Hsia
Department of Aeronautics and Astronautics,National Cheng Kung University,Tainan 701,Taiwan,Republic of China
国际会议
长沙
英文
1095-1100
2014-05-31（万方平台首次上网日期，不代表论文的发表时间）