Spectral Theory and Quantum Mechanics

Mathieu Lewin is CNRS research director (Directeur de Recherche) at Paris-Dauphine University. He specialises in spectral and variational methods in quantum systems.

• 1 Introduction to quantum mechanics: the hydrogen atom.- 2 Self-adjointness.- 3 Self-adjointness criteria: Rellich, Kato & Friedrichs.- 4 Spectral theorem and functional calculus.- 5 Spectrum of self-adjoint operators.- 6 N-particle systems, atoms, molecules.- 7 Periodic Schrödinger operators, electronic properties of materials.- Appendix A: Sobolev spaces.- Appendix B: Problems.