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

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  • Gergely Palla
  • Gábor Vattay
  • József Cserti

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.

Suggested Citation

  • Gergely Palla & Gábor Vattay & József Cserti, 2001. "Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 26, pages 1-12, January.
    • Handle: RePEc:hin:jijmms:314053
    DOI: 10.1155/S0161171201020129
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