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The quantum spectra are derived from the wave-functions and the energy-functions of the isosceles-right triangular model. Although the eigenstates of the billiard system are not separable, the problem of functions with two variables is exactly solvable. The numerical results of the Fourier transform of quantum spectral functions are compared with the results from the classical orbits whose lengths match well with the positions of the spectra peaks. This result gives a new evident for the correspondence of quantum and classical mechanics.
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Keywords:
- isosceles-right triangle /
- quantum spectra /
- classical orbits /
- quantum billiard
[1] Esaki L, Tus R 1970 IBMJ Res. Dev. 14 61
[2] Gutzwiller MC 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
[3] Liao Q H, Liu Z D, You S P, Cao C Q 2007 Acta Sinica Quantum Optica 13 304 (in Chinese) [廖庆洪, 刘正东, 尤素萍, 曹昌祺 2007 量子光学学报 13 304]
[4] Huang G M, Liu Y M 2009 Journal of Atomic and Molecular Physics 26 447 (in Chinese) [黄钢明 刘益民2009 原子与分子 26 447]
[5] Zhang L Q, Zhang Y H, Xu X Y, Wang Y J, Lin S L, Du M L 2007 Journal of Atomic and Molecular Physics 24 69 (in Chinese) [张丽琴, 张延惠, 徐学友, 王雅静, 林圣路, 杜孟利 2007 原子与分子 24 69]
[6] Zhu M Z, Wang Z X, Mei C 2011 Journal of Atomic and Molecular Physics (in press) (in Chinese) [朱满座, 王志霞, 梅超2011 原子与分子 (in press)]
[7] Jun L 2008 Progress in Nature Science 18 927
[8] Robinett R W 1998 Math. Phys. 39 278
[9] Robinett R W 1997 Am. J. Phys. 65 1167
[10] Lu J, Du M L 2004 Acta Phys. Sin. 53 2450 (in Chinese) [陆军, 杜孟丽 2004 53 2450]
[11] Lin S L, Gao F, Hong Z P, Du M L 2004 Chin. Phys. Lett. 22 9
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[1] Esaki L, Tus R 1970 IBMJ Res. Dev. 14 61
[2] Gutzwiller MC 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
[3] Liao Q H, Liu Z D, You S P, Cao C Q 2007 Acta Sinica Quantum Optica 13 304 (in Chinese) [廖庆洪, 刘正东, 尤素萍, 曹昌祺 2007 量子光学学报 13 304]
[4] Huang G M, Liu Y M 2009 Journal of Atomic and Molecular Physics 26 447 (in Chinese) [黄钢明 刘益民2009 原子与分子 26 447]
[5] Zhang L Q, Zhang Y H, Xu X Y, Wang Y J, Lin S L, Du M L 2007 Journal of Atomic and Molecular Physics 24 69 (in Chinese) [张丽琴, 张延惠, 徐学友, 王雅静, 林圣路, 杜孟利 2007 原子与分子 24 69]
[6] Zhu M Z, Wang Z X, Mei C 2011 Journal of Atomic and Molecular Physics (in press) (in Chinese) [朱满座, 王志霞, 梅超2011 原子与分子 (in press)]
[7] Jun L 2008 Progress in Nature Science 18 927
[8] Robinett R W 1998 Math. Phys. 39 278
[9] Robinett R W 1997 Am. J. Phys. 65 1167
[10] Lu J, Du M L 2004 Acta Phys. Sin. 53 2450 (in Chinese) [陆军, 杜孟丽 2004 53 2450]
[11] Lin S L, Gao F, Hong Z P, Du M L 2004 Chin. Phys. Lett. 22 9
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