In the first lecture of this seminar, I will give you an introduction to semiclassical analysis, concerning basic tools of pseudodifferential calculus, quantum limits, semiclassical measures, construction of quasimodes, and related topics. We will pay special attention to some well establish examples of completely integrable systems to exercise the tools and ideas introduced.

In the second lecture, I will present you some new results concerning the semiclassical limit of sequences of eigenfunctions for small perturbations of completely integrable systems. To deep in the proofs, we will use some of the tools introduced in the first talk together with some KAM techniques.

Part of this work has been obtained in collaboration with Fabricio Macià.