论文标题
对一维schrödinger方程中的最低本本函数采样以恢复电势
Sampling The Lowest Eigenfunction to Recover the Potential in a One-Dimensional Schrödinger Equation
论文作者
论文摘要
我们考虑bvp $ -y“ + qy =λy$，$ y（0）= y（0）= y（1）= 0 $。逆频谱问题要求一个人从光谱信息中恢复$ q $。在本文中，我们提供了一种非常简单的方法来恢复潜在的方法，可以通过对一个特征功能进行采样来恢复潜在的频谱。频谱的相对范围是较大的信息。 \ textit {增加}），因此使用较低模式的数据也使我们可以从\ textit {一}边界条件中恢复“任何”潜力。
We consider the BVP $-y" + qy = λy$ with $y(0)=y(1)=0$. The inverse spectral problems asks one to recover $q$ from spectral information. In this paper, we present a very simple method to recover a potential by sampling one eigenfunction. The spectral asymptotics imply that for larger modes, more and more information is lost due to imprecise measurements (i.e. relative errors \textit{increases}) and so it is advantageous to use data from lower modes. Our method also allows us to recover "any" potential from \textit{one} boundary condition.
