Quantum Dynamics: Spectral Decomposition

This lecture covers the decomposition of the Hilbert space into spectral types and explores basic results in quantum dynamics, such as the Riemann-Lebesgue lemma and Wiener's theorem. The slides discuss the realization of the decomposition by writing specific equations and the implications for quantum systems. The lecture also delves into the concept of A-invariance and the mathematical interpretation of the spectral types. The application of these concepts is demonstrated through various examples and proofs, highlighting the significance of spectral decomposition in quantum mechanics.