16. listopadu - 22. listopadu
Osnova sekce
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- Expression for S-matrix in terms of Jost functions
- Regular solution and its relation to Jost functions
- Analyticity of the Regular solution
- Analytic continuation of Jost functions into complex plane
- Regions of analyticity of Jost functions and the S-matrix
- Extensions of analyticity for short-range potentials
- Distribution of poles of the S-matrix in the complex plane
- Resonances, virtual states, bound states as poles of the S-matrix
- Breit-Wigner form of resonant scattering cross section and phase shift
- Signatures of resonances and virtual states in scattering cross sections and phase shifts
- Riemann surface of S-matrix in complex energy plane: physical vs unphysical sheets.
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- Classical scattering asymptotes and orbits vs quantum in/out asymptotic and scattering states
- Unitary vs Isometric operators
- Asymptotic condition, assumptions on the scattering potentials, orthogonality theorem
- Intertwining relations for Moeller operators and implication for conservation of energy in scattering.
- S-matrix and its decomposition using scattering amplitude
- Calculation of quantum cross section in momentum space
- Optical theorem
- Derivation of T-matrix elements and scattering amplitude from TD point of view and connection with the stationary theory
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