Proof of Weyl's Theorem

This lecture covers the proof of Weyl's theorem, discussing the discrete spectrum of the harmonic oscillator accumulating at infinity, ground states, and ground state energy of Schrödinger operators. It also explores the weak continuity of the potential energy, emphasizing the compactness of the resolvent and the localization of the potential to apply the Rellich-Kondrachov theorem. The lecture concludes with the identification of the purely discrete spectrum and the minimizers of the ground state energy. Various mathematical arguments and approximations are used to demonstrate the properties of the spectrum and the energy levels.