本論文從亥姆霍茲方程式( Helmholtz Equation)出發，運用有限元素法解出系統穩態波函數，再輸入Husimi Function構建出相空間的資訊。為了能提供更直觀的物理感覺，我們以半古典的方法將向空間分布函數投影到邊界上得到龐卡萊截面(Poincare Section)上的機率密度，澄清其物理意義。基於這些結果，我們研究光學系統中的穩態解。

We start from the Helmholtz Equation, using Finite-Element Method to solve the stationary solutions ,and construct the information in phase space using Husimi function . To get more direct physical insights , we map the phase space distribution on the Poincare Section of Surface ,and give the handled phase space distribution physical interpretations . Finally, we use it to get more physical insights in some special systems. Based on these results ,we study the stationary states in optical cavities .

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