Fixed Energy Propagator: Analytic Structure and Applications

This lecture delves into the concept of the fixed energy propagator, explaining its definition as a Fourier transform of the retarded propagator. The instructor discusses the analytic structure of the propagator in the complex energy plane, highlighting its connection with the retardation property. The lecture explores the computation of the fixed energy propagator for both negative and positive energies, emphasizing the boundary conditions required for its determination. Additionally, the lecture demonstrates how the fixed energy propagator can be used to compute the density of states and analyze the probability of barrier penetration in quantum systems.