On the spectrum of the Schrödinger operator with large potential concentrated on a small set (Q2473687)

This paper studies the simple eigenvalues of Schrödinger operators on a bounded domain of \(\mathbb{R}^n\) when the potential is large, smooth and increasingly concentrated on a small set. Its main result gives an explicit formula for the first order term of the asymptotic expansion of these eigenvalues as perturbations of simple eigenvalues of the Laplace operator. A corresponding asymptotic formula for the eigenfunctions is also provided.