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

Gergely Palla, Gábor Vattay and József Cserti

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 26, 1-12

Abstract:

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 ħ 2 , therefore a discrepancy between different semiclassical trace formulas in order of ħ 2 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.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:314053

DOI: 10.1155/S0161171201020129

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