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Springer eBooks

Scattering Theory

Alberto Galindo, P. Pascual

Published Jan 1, 1991• 0 citations
Publisher
DOI
10.1007/978-3-642-84129-3_1

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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.
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.
The possibility of constructing a nonrelativistic scattering theory without appealing to the Schroedinger formalism is investigated, the theory being based on the general physical principles of causality, superposition, and unitarity. It is proved that the proposed approach is more general than the nonrelativistic scattering theory based on the Schroedinger equation. The proposed approach is used for the construction of a model scattering theory for a system consisting of heavy nonrelativistic particles and a light relativistic particle.