軌跡論與機率論是量子力學的二種不同詮釋。複數力學透過複數軌跡的疊加，證實所得軌跡落點的統計分布與機率論的預測相符，從而統一了軌跡論與機率論二種詮釋。然而這二種詮釋的一致性目前仍存在著二種細微的偏差。第一種偏差是源自求解複數軌跡的數值誤差，第二種偏差是源自複數軌跡樣本數不足所產生的統計誤差，而本論文的目的即在提出解決之道，分別克服這二種誤差。
對於求解複數力學隨機微分方程式所產生的數值誤差，本論文引入歐拉-丸山(Euler-Maruyama)方法，這是一種專門求解隨機微分方程式的數值方法，用以取代傳統的ODE45方法。這一方法的引入除了獲得較好的數值精確度外，在數值計算的效率上也大幅提升。在另一方面，對於複數軌跡樣本數不足所產生的統計誤差，本論文透過Fokker-Planck PDE方程式的求解，直接獲得描述軌跡落點的機率密度函數，而不需以疊加數萬條軌跡的方式去取得統計資料，從而避開了因樣本數不足所產生的統計誤差。本論文針對統計力學與複數力學所對應的Fokker-Planck PDE，利用有限差分法加以求解，所得結果證實複數軌跡的純實部落點統計曲線會與統計力學所對應的Fokker-Planck PDE的解相同，而複數軌跡的實部投影統計曲線則會與複數力學所對應的Fokker-Planck PDE的解一致。

Trajectory interpretation and probability interpretation are two opposite interpretations of quantum mechanics. The complex mechanics unifies the two interpretations by showing that the distribution of the collected trajectory points follows the statistic pattern predicted by the probability interpretation. However, there still exist slight discrepancies between the two interpretations. The first discrepancy comes from the numerical errors in the computation of trajectory points, while the second comes from the statistical error caused by the inadequacy of the adopted sample space of trajectories. The aim of this thesis is to provide workable methods to remedy the discrepancies.
Regarding the numerical errors in generating trajectory points by solving stochastic differential equations (SDE), we adopt the Euler-Maruyama method, which is specialized in solving SDE, to replace the conventional ODE45 method, and remarkable reductions in computation error and computation time have been observed. On the other hand, regarding the statistical error caused by the inadequacy of the adopted sample space of trajectories, we obtain directly the probability density function (PDF), which describes the distribution of the collected trajectory points, by solving the associated Fokker-Planck PDE. This approach allows us to obtain the PDF without having to generate thousands of trajectories to form the required sample space. The Fokker-Planck PDE is solved by finite difference method and the solutions are found to be consistent with the distributions of trajectories computed by statistic mechanics and complex mechanics.

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