Sylabus
1. Preliminaries: reminders on formalism of quantum mechanics, states and operators
1.1 Linear space and metrics
1.2 Hermitian operators, projection operators, inverse operators, unitary operators
2. The formal theory of scattering
2.1 The cross section and other observables
2.2 The Schrodinger, Heisenberg and interaction pictures
2.3 Perturbation theory in the interaction representation
2.4 The Moller's operators and the Lippmann-Schwinger equations
2.5 S and T matrices
3. Solution of the Schrodinger equation for scattering states
3.1 The semi-classical (WKB) approximation
3.2 Green's functions, the Born approximation and the stationary scattering states
3.3 The transfer matrix method
3.4 R-matrix approach to scattering
3.5 Application 1: One-dimensional scattering
3.6 Application 2: The two-dimensional case
3.7 Application 3: Three-dimensional scattering from a central potential, partial wave expansion and the concept of phase shift
3.8 Application 4: The Korringa-Kohn-Rostoker method for band structure calculation in solids
4. The time-dependent approach to scattering
4.1 Floquet theory
4.2 Feshbach's decay theory
4.3 Time-dependent variational method
4.4 Time propagation by numerical integration and evolution operator
4.5 Scattering wave-functions by wave-packet propagation
4.6 Application 1: Photoionization of atoms in intense laser field
4.7 Application 2: Electron-molecule scattering and the case of the dissociative attachment of molecules
5. The time-independent approach to scattering
5.1 Fano's decay theory and the continuum-discrete interaction
5.2 The projected resolvent
5.3 The two-potential scattering
5.4 Multichannel scattering theory
5.5 Application 1: Electron spectroscopy of molecules as an example of multichannel scattering
5.5 Application 2: BEC-BCS crossover of ultra-cold Fermi gases at unitarity
5.7 Application 3: Theory of electron capture and beta decay in stellar nucleosynthesis Bibliography
1. \Scattering Theory: The Quantum Theory of Nonrelativistic Collisions", John R. Taylor - Dover Books on Engineering (2006)
2. \Scattering Theory of Waves and Particles: Second Edition", Roger G. Newton - Dover Books on Physics (2013)
3. Further notes given by the lecturer during the course