在量子力學中，只能從粒子波函數之機率分佈來說明粒子可能出現的位置，而無法得到粒子的真實運動軌跡。在本論文中，利用複數力學之架構，將古典位勢能Rosen-Morse Potential 代入複數力學中，可以產生(Hamilton-jacobi) H-J 方程式獲得氨分子在複數空間下之運動軌跡。將古典位勢能加上複數力學之量子位勢能(quantum potential)後所產生之總位勢能才是粒子所真實遭遇到的真正位勢能，此總位勢能得以合理解釋粒子的機率分佈。本論文將Rosen-Morse Potential應用至氮原子在氨分子中所受之雙最低點位勢，由氮原子在複數空間下之運動軌跡，求出其穿隧範圍及振動頻率，並與實驗所得之氨分子振動頻率作比較。

In quantum mechanics, particle’s motion can only described by probability density function; there is no related equation of motion that can be solved to find the particle’s trajectory. In this thesis, the Rosen-Morse (R-M) potential is studied in the framework of complex mechanics and the Hamilton equations of motion are derived to find the ammonia molecular quantum motion in complex space. The summation of the R-M potential and the quantum potential form the total potential that governs the quantum motion and explains the probability distribution of ammonia molecules. There are two equilibrium positions for the nitrogen atom in the ammonia molecule. The vibration of the nitrogen atom about its equilibrium positions are analyzed in terms of its trajectories solved from the Hamilton equations of motion. The vibration periods are computed by residue theorem and compared with the experimental measurement.

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