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求解薛定谔方程

使用数值方法求解薛定谔方程,可以先运行test文件来进行简单的运行测试。
薛定谔方程为:
$$\frac{-\hbar^2}{2m}\frac{d^2}{dx^2}\psi+V\psi=E\psi$$ 化简为:
$$(\frac{-\hbar^2}{2m}\frac{d^2}{dx^2}+V)\psi=E\psi$$
即:
$$H\psi=E\psi$$
哈密顿量为:
$$H=\frac{-\hbar^2}{2m} \left( \begin{array}{ccc} -2& 1& 0& 0& \ 1& -2& 1& 0& \ 0& 1& -2& 1& \ & & ...& ...& ...\ & & & 1& -2\ \end{array}\right)$$ 矩阵部分即为二阶差分,以用来数值求解薛定谔方程。
二阶差分:
$$f'=(f_{i+1}-2f_i+f_{i-1})/h^2$$

一维无限深方势阱/Infinite_Square_Well

在m设为1,hbar设为1,势阱为-1/2到1/2的情况下,利用二阶差分求解薛定谔方程。

一维有限深方势阱/Finite_Square_Well

基本方法与一维无限深方势阱一致,m设为1,hbar设为1,势阱范围为-a/2-a/2,其中-b/2-b/2为V=-6,其余为0,求前五个值(若有散射态,舍去)

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