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(∣x∣) is a known increasing radial potential satisfying lim∣x∣→+∞q(∣x∣)=+∞ and V(x) is a bounded potential