TY - JOUR
T1 - The accuracy of semiclassical quantization for an integrable system - The hyperspherical billiard
AU - Rahav, Saar
AU - Agam, Oded
AU - Fishman, Shmuel
PY - 1999/10/15
Y1 - 1999/10/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0033569257&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/32/41/305
DO - 10.1088/0305-4470/32/41/305
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AN - SCOPUS:0033569257
SN - 0305-4470
VL - 32
SP - 7093
EP - 7107
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 41
ER -