Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach
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...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201020129 |
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| author | Gergely Palla Gábor Vattay József Cserti |
| author_facet | Gergely Palla Gábor Vattay József Cserti |
| author_sort | Gergely Palla |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-bff930093722450784cb1104b7406d8c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-bff930093722450784cb1104b7406d8c2025-02-03T05:45:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126526928010.1155/S0161171201020129Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approachGergely Palla0Gábor Vattay1József Cserti2Department of Physics of Complex Systems, Eötvös University, Pázmány Péter sétany 1/A, Budapest H-1117, HungaryDepartment of Physics of Complex Systems, Eötvös University, Pázmány Péter sétany 1/A, Budapest H-1117, HungaryDepartment of Physics of Complex Systems, Eötvös University, Pázmány Péter sétany 1/A, Budapest H-1117, HungarySemiclassical 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.http://dx.doi.org/10.1155/S0161171201020129 |
| spellingShingle | Gergely Palla Gábor Vattay József Cserti Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach International Journal of Mathematics and Mathematical Sciences |
| title | Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach |
| title_full | Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach |
| title_fullStr | Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach |
| title_full_unstemmed | Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach |
| title_short | Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach |
| title_sort | semiclassical quantization of circular billiard in homogeneous magnetic field berry tabor approach |
| url | http://dx.doi.org/10.1155/S0161171201020129 |
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