Asymptotics of eigenelements of boundary value problems for the Schrödinger operator with a large potential localized on a small set

Asymptotics of eigenelements of a singularly perturbed boundary value problem for the three-dimensional Schrödinger operator is constructed in a bounded domain with the Dirichlet and Neumann boundary condition. The perturbation is described by a large potential whose support contracts into a point. In the case of the Dirichlet boundary conditions, this problem corresponds to a potential well with infinitely high walls and a narrow finite peak at the bottom.