Spectral properties of Schrödinger operators on domains with varying orders of thinness (Q1382713)

The author studies the behavior of the eigenvalues and of the eigenfunctions of Schrödinger operators defined on domains depending on a small parameter: thin domains with varying orders of thinness or on dumbbell domains. In both situations, he compares the eigenvalues and the eigenfunctions with the ones of a ``limit operator'' defined on a ``limit domain''.