The inverse nodal problem for perturbed spherical Schrödinger operator defined on (0, 1) is studied. We prove that the potential on the whole interval can be uniquely determined in terms of a twin dense nodal subset known on the interior subinterval \((a,1),a \in (0,1).\) Especially, when \(a \in \left( \frac{1}{2},1\right) ,\) we need additional spectral information, which is associated with the derivatives of eigenfunctions at some known nodal points.

中文翻译：

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扰动球形薛定谔算子的逆节点问题

研究了(0, 1)上定义的扰动球形薛定谔算子的逆节点问题。我们证明整个区间上的势可以根据内部子区间 \((a,1),a \in (0,1).\)上已知的孪生密集节点子集唯一确定。特别是，当\( a \in \left( \frac{1}{2},1\right) ,\)我们需要额外的光谱信息，这些信息与某些已知节点处的本征函数的导数相关。