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Focal points and the phase of the semiclassical propagator

Authors
Journal
Annals of Physics
0003-4916
Publisher
Elsevier
Publication Date
Volume
114
Identifiers
DOI: 10.1016/0003-4916(78)90268-3
Disciplines
  • Mathematics

Abstract

Abstract The relation between the phase of the semiclassical propagator and the number of times the classical trajectory is reflected from a caustic is discussed. It is shown that the accepted prescription based on Morse's focal point theorem is valid only for a restricted class of problems (coordinate representation and a positive definite mass tensor). A more general method to evaluate the phase is derived. It applies to all problems of physical interest involving the most general representations (mixed coordinate and momentum) and complicated Hamiltonian functions. The result is of particular relevance for the classical S-matrix.

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