Calculating the bound spectrum by path summation in action-angle variables

M. V. Berry, M. Tabor

Research output: Contribution to journalArticlepeer-review

213 Scopus citations


The density of states n(E) is calculated for a bound system whose classical motion is integrable, starting from an expression in terms of the trace of the time-dependent Green function. The novel feature is the use of action-angle variables. This has the advantages that the trace operation reduces to a trivial multiplication and the dependence of n(E) on all classical closed orbits with different topologies appears naturally. The method is contrasted with another, not applicable to integrable systems except in special cases, in which quantization arises from a single closed orbit which is assumed isolated and the trace taken by the method of stationary phase.

Original languageEnglish (US)
Article number009
Pages (from-to)371-379
Number of pages9
JournalJournal of Physics A: General Physics
Issue number3
StatePublished - 1977
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics


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