Focal points and the phase of the semiclassical propagator

S. Levit*, K. Möhring, U. Smilansky, T. Dreyfus

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)223-242
Number of pages20
JournalAnnals of Physics
Issue number1-2
StatePublished - 1 Sep 1978
Externally publishedYes


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