The spectrum of the Laplacian operator is well known: its a purely absolutely continuous spectrum without eigenvalue. But What happen if we add to the Laplacian a potential.
In this talk, we will show some properties of the spectrum of Schrödinger operators (nature of the spectrum and Limiting Absorption Principle) when the potential is "small" with respect to the Laplacian. To do this, we will recall the Mourre Theorem in a first part. In the following, we will show different ways to use apply this theorem to Schrödinger operators. To finish this talk, we will give some examples of singular potentials for which we can use the Mourre Theorem.