On the eigenvalues of a Schrödinger operator

The aim of this thesis is to obtain an asymptotic formula for the eigenvalues of the self adjoint Schrödinger operator defined on the space of Lebesgue integrable functions over the domain F with the given mixed boundary condition defined on a d-dimensional parallelepiped F. First, the eigenvalues and the eigenfunctions of the unperturbed operator are found. The ddimensional real space is divided into two domains as non-resonance and resonance domains. The eigenvalues of the unperturbed operator are divided into two groups as non-resonance and resonance with respect to these domains. The asymptotic formula for the non-resonace eigenvalues of the perturbed operator is obtained by using the binding formula.