Quantum Mechanics: Spectral Basis and Schrödinger Equation

This lecture covers the proof of the existence of a spectral basis and the solution to the Schrödinger equation. It delves into the concept of unitary equivalence and the generation of self-adjoint operators. The instructor demonstrates the process of constructing a spectral basis iteratively and the properties of unitary one-parameter groups. The lecture concludes with the unique solution to the Schrödinger equation and the strong continuity of unitary groups. Various mathematical proofs and definitions are provided to support the theoretical concepts discussed.