  This is the proceeding of a talk given in Workshop on Differential Geometry
and its applications at Alexandru Ioan Cuza University Ia\c{s}i, Romania,
September 2--4, 2009. I explain how positive commutator estimates help in the
analysis of embedded eigenvalues in a geometrical setting. Then, I will discuss
the disappearance of eigenvalues in the perturbation theory and its relation
with the Fermi golden rule.
