The accuracy of semiclassical quantization for an integrable system - The hyperspherical billiard

Saar Rahav*, Oded Agam, Shmuel Fishman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The eigenvalues of the hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics that approach the wall of the billiard. The fraction of energy levels for which the semiclassical error is larger than some given value is calculated analytically (and tested numerically) and found to be independent of energy. The implications for other systems, in particular integrable ones, are discussed.

Original languageAmerican English
Pages (from-to)7093-7107
Number of pages15
JournalJournal of Physics A: Mathematical and General
Volume32
Issue number41
DOIs
StatePublished - 15 Oct 1999

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