International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 5, Pages 269-280

Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach

Gergely Palla, Gábor Vattay, and József Cserti

Department of Physics of Complex Systems, Eötvös University, Pázmány Péter sétany 1/A, Budapest H-1117, Hungary

Received 7 November 2000; Revised 9 April 2001

Copyright © 2001 Gergely Palla et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Semiclassical methods are accurate in general in leading order of ħ, since they approximate quantum mechanics via canonical invariants. Often canonically noninvariant terms appear in the Schrödinger equation which are proportional to ħ2, therefore a discrepancy between different semiclassical trace formulas in order of ħ2 seems to be possible. We derive here the Berry-Tabor formula for a circular billiard in a homogeneous magnetic field. The formula derived for the semiclassical density of states surprisingly coincides with the results of Creagh-Littlejohn theory despite the presence of canonically noninvariant terms.