Quantum Spectra and Classical Orbits in Two-Dimensional Equilateral Triangular Billiards
LIN Sheng-Lu1, GAO Feng1,2, HONG Zheng-Pin1, DU Meng-Li3
1Department of Physics, Shandong Normal University, Jinan 250014
2Division of Physics, Shandong Agriculture University, Taian 271000
3Institute of Theoretical physics, Chinese Academy of Sciences, PO Box 2735, Beijing 100080
Quantum Spectra and Classical Orbits in Two-Dimensional Equilateral Triangular Billiards
LIN Sheng-Lu1;GAO Feng1,2;HONG Zheng-Pin1;DU Meng-Li3
1Department of Physics, Shandong Normal University, Jinan 250014
2Division of Physics, Shandong Agriculture University, Taian 271000
3Institute of Theoretical physics, Chinese Academy of Sciences, PO Box 2735, Beijing 100080
Abstract： We study the correspondence between quantum spectra and classical orbits in the equilateral triangular billiards. The eigenstates of such systems are not separable functions of two variables even though the problem is exactly solvable. We calculate the Fourier transform of a quantum spectral function and find that the positions of the peaks match well with the lengths of the classical orbits. This is another example showing that the quantum spectral function provides a bridge between quantum and classical mechanics.
2005, Vol. 22 
