我們考慮一維的薛丁格方程 (Schrödinger equation)， 並求其最低能階。 在本文中我們僅討論其波函數(特徵函數)為軸對稱(radius symmetric)的情形。 關於質量的逼近， 我們使用非拋物線的有效質量近似 (non-parabolic
effective mass approximation)。

這裡主要的工作是將一維薛丁格方程離散化後轉變成---有理多項式， 或多項式型矩陣特徵值問題， 並且讓其係數矩陣為對稱， 之後利用一些數值方法去找出最小的正特徵值。

We consider one dimension Schrödinger Equation,and find the lowest energy. In this paper, we only discuss the case of that the wave function is radius symmetric. About the approximation of the mass, we use non-parabolic effective mass approximation.

Here, our work is to transform 1-D Schrödinger Equation forming a eigenvalue problem of a rational form or a polynomial form, and then let the coefficient matrix be symmetric. After that using some numerical methods find out the smallest positive eigenvalue.

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