The Theory of Scattering

敏夫 加藤, 成俊 黒田

Michael A. Morrison, Andrew N. Feldt

Four ambiguities are inherent in time-independent quantum-mechanical scattering theory: two in the normalization of continuum functions, and two in the relation between various scattering matrices. These ambiguities allow the use of different conventions in scattering theory. This freedom has led to inconsistencies among textbooks, monographs, review articles, and research papers. We identify these ambiguities, indicate their context and origin in scattering theory, give the key equations of scattering theory in a form that can by adapted to any convention, and show interrelations between these equations that can lead to confusion and error. We also give several diagnostic approaches for determining the conventions used in a particular source, and reference conventions adopted in widely used books on scattering theory.

V. K. Ignatovich

The standard scattering theory (SST) in non relativistic quantum mechanics (QM) is analyzed. Self-contradictions of SST are deconstructed. A direct way to calculate scattering probability without introduction of a finite volume is discussed. Substantiation of SST in textbooks with the help of wave packets is shown to be incomplete. A complete theory of wave packets scattering on a fixed center is presented, and its similarity to the plane wave scattering is demonstrated. The neutron scattering on a monatomic gas is investigated, and several problems are pointed out. A catastrophic ambiguity of the cross section is revealed, and a way to resolve this ambiguity is discussed.

Günther Ludwig

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 ...

Felix Alexandrovich Berezin, M A Shubin