延續德布洛伊導引波的概念，本論文將量子力學視為隨機最佳導引律的問題。在量子世界當中，吾人可將電子看做一架被導引的飛行器，而伴隨其身的導引波正是在追隨由維納程序所驅動的隨機標靶時並且同時在最小化剩餘成本函數考量之下，所設計出來的導引律。在藉由動態規劃法求解隨機最佳導引問題之後，吾人指出導引粒子運動的最佳導引波，其實就是薛丁格方程式的解：波函數 。同時間，吾人發現閉迴路導引系統形成波函數 之複數狀態空間動態，而量子算符便自然地從中而生。文章末吾人將求解在最佳導引律作用之下的量子軌跡，並顯示其在實數空間中的統計分佈與機率密度函數 的預測一致。

Following the de Broglie’s idea of pilot wave, this dissertation 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 , a solution to Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state-space dynamics for , from which quantum operators emerge naturally. 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 .

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