Weyl’s law (1911) describes the asymptotic distribution of the eigenvalues of an elliptic differential operator in terms of the geometry of the underlying domain or manifold. In this talk, we study eigenvalue problems for Schrödinger operators with inverse-square potentials on conic surfaces. Using highly accurate spectral solvers, we compute a large number of eigenvalues and formulate a conjectural Weyl-type law. Its asymptotic behavior and geometric dependence differ from those in the standard smooth setting, revealing the combined effects of the singular potential and the conic geometry. We then provide a rigorous proof of the proposed law. This is a joint work with Jiantao Jiang (Beijing CSRC) and Zhimin Zhang (Wayne State University).