Comparison of Atomic and Molecular Trajectories under Optimal Stochastic Control with Quantum Probability

• Main Authors: Lin-YuLiu, 劉林育
• Other Authors: Ciann-Dong Yang
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/36399052828702790641

碩士 === 國立成功大學 === 航空太空工程學系碩博士班 === 101 === The purpose of this paper is to establish a state-space for quantum systems, according to optimal stochastic control, and to verify that a quantum system is actually an optimized stochastic system. The proposed optimization process comprises two steps: complexification and randomization, and the outcome of the process shows that a quantum motion is actually a complex Brownian motion. After our study, it becomes clear that a quantum path is random and fractal, and is governed by a stochastic differential equation, from which a quantum paths can be solved for electronic motions in hydrogen atom and for orbital angular momentum and quantum dynamics in diatomic molecules.