Předmět Scattering methods for nuclear and condensed matter research (NJSF147)

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Materiál	Typ	Datum	Počet stažení

Sylabus

1. Preliminaries: reminders on formalism of quantum mechanics, states and operators1.1 Linear space and metrics1.2 Hermitian operators, projection operators, inverse operators, unitary operators2. The formal theory of scattering2.1 The cross section and other observables2.2 The Schrodinger, Heisenberg and interaction pictures2.3 Perturbation theory in the interaction representation2.4 The Moller's operators and the Lippmann-Schwinger equations2.5 S and T matrices3. Solution of the Schrodinger equation for scattering states3.1 The semi-classical (WKB) approximation3.2 Green's functions, the Born approximation and the stationary scattering states3.3 The transfer matrix method3.4 R-matrix approach to scattering3.5 Application 1: One-dimensional scattering3.6 Application 2: The two-dimensional case3.7 Application 3: Three-dimensional scattering from a central potential, partial wave expansionand the concept of phase shift3.8 Application 4: The Korringa-Kohn-Rostoker method for band structure calculation in solids4. The time-dependent approach to scattering4.1 Floquet theory4.2 Feshbach's decay theory4.3 Time-dependent variational method4.4 Time propagation by numerical integration and evolution operator4.5 Scattering wave-functions by wave-packet propagation4.6 Application 1: Photoionization of atoms in intense laser field4.7 Application 2: Electron-molecule scattering and the case of the dissociative attachment of molecules5. The time-independent approach to scattering5.1 Fano's decay theory and the continuum-discrete interaction5.2 The projected resolvent5.3 The two-potential scattering5.4 Multichannel scattering theory5.5 Application 1: Electron spectroscopy of molecules as an example of multichannel scattering5.5 Application 2: BEC-BCS crossover of ultra-cold Fermi gases at unitarity5.7 Application 3: Theory of electron capture and beta decay in stellar nucleosynthesisBibliography1. 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

Garant

Alfredo Iorio, Ph.D.