Osnova sekce

      • 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.
      • 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