本文主要是討論關於非均勻位勢方程的一些固有值問題。
在非均勻位勢方程式中，當密度函數與位能函數皆為週期函數時，若其第一個Neumann固有值函數為常數函數時，我們可得知密度函數與位能函數呈現一倍數關係。若其第一個Neumann固有值函數為常數函數，所有Dirichlet固有值函數皆為常數函數，則密度函數與位能函數皆為常數函數。
在非均勻位勢方程式中，當密度函數與位能函數不為週期函數時，若其第一個Neumann固有值為0時，且其所有Dirichlet固有值與Neumann固有值皆相等時，我們可知密度函數的一些性質以及位能函數和密度函數之間的關係。

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