Potential Scattering Theory

Arne Jensen

Adam Lupu-Sax

Scattering theory provides a convenient framework for the solution of a variety of problems. In this thesis we focus on the combination of boundary conditions and scattering potentials and the combination of non-overlapping scattering potentials within the context of scattering theory. Using a scattering t-matrix approach, we derive a useful relationship between the scattering t-matrix of the scattering potential and the Green function of the boundary, and the t-matrix of the combined system, effectively renormalizing the scattering t-matrix to account for the boundaries. In the case of the combination of scattering potentials, the combination of t-matrix operators is achieved via multiple scattering theory. We also derive methods, primarily for numerical use, for finding the Green function of arbitrarily shaped boundaries of various sorts. These methods can be applied to both open and closed systems. In this thesis, we consider single and multiple scatterers in two dimensional strips ...

R. Gagnon

Scattering theory for extended elementary particles in stochastic phase space is studied. It is shown that the interacting Hamiltonian is equivalent to an effective potential in configuration representation. Asymptotic completeness can be studied by investigating the behavior of the effective potential. The sharp-point limit of the extension of these particles is studied. It is also shown that scattering theory can also be studied directly in stochastic phase space in the optimal case.

Willi-Hans Steeb