Spectral Density: Semiclassical Approximation

This lecture covers the semiclassical approximation for the spectral density, including the Bohr-Sommerfeld quantization condition and the fixed energy propagator as a sum over multiple saddle points. The instructor explains the application of barrier penetration and the calculation of transmission probability using phase space with energy considerations. The lecture delves into the spectral density concept, recalling the quantization condition and discussing the semiclassical approximation for various scenarios. The importance of saddle points in the semiclassical approximation is highlighted, along with the corrections needed for accurate results. The lecture concludes with a detailed explanation of the Bohr-Sommerfeld quantization condition and its significance in quantum mechanics.