An inverse spectral problem for a schrodinger operator with unbounded potential

Abstract

In this paper, we prove a uniqueness theorem for the potential $V(x)$ of the following Schrödinger operator H=-\Delta +q(\vert x \vert)+V(x) \mbox{ in } \mathbb{R}^2, where $q(\vert x \vert)$ is a known increasing radial potential satisfying $\lim_{\vert x \vert \rightarrow + \infty}q(\vert x \vert)= +\infty$ and $V(x)$ is a bounded potential