Chinese Physics C > 2001, Vol. 25 > Issue(10): 958-963

Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System

SONG Jian-Jun^,,
LI Xi-Guo

Research Center of theoretical Nuclear Physics, Teh National Laboratory of Heavy Ion Collision, Lanzhou 730000, China2 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

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Abstract：
The general quantization condition for periodic orbits in a two-dimensional integrable sys- tem is presented via the Berry-Tabor trace formula. Using the quantization and a periodicity condi- tion of periodic orbits the semiclassical quantization condition and semiclassical quantized energies of a two dimensional uncoupled quartic oscillator system are given in detail. The semiclassical quantized energies-periodic orbits correspondence is also analysed.

References

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SONG Jian-Jun and LI Xi-Guo. Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System[J]. Chinese Physics C, 2001, 25(10): 958-963.

SONG Jian-Jun and LI Xi-Guo. Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System[J]. Chinese Physics C, 2001, 25(10): 958-963. shu

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Received: 2000-10-17
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

Trace Formula and Periodic Orbits Quantization for Two-Dimensional Integrable System

SONG Jian-Jun^,
LI Xi-Guo

Corresponding author:SONG Jian-Jun,

Research Center of theoretical Nuclear Physics, Teh National Laboratory of Heavy Ion Collision, Lanzhou 730000, China2 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China

Received Date:2000-10-17
Accepted Date:1900-01-01
Available Online:2001-10-05

Abstract:The general quantization condition for periodic orbits in a two-dimensional integrable sys- tem is presented via the Berry-Tabor trace formula. Using the quantization and a periodicity condi- tion of periodic orbits the semiclassical quantization condition and semiclassical quantized energies of a two dimensional uncoupled quartic oscillator system are given in detail. The semiclassical quantized energies-periodic orbits correspondence is also analysed.