Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1997-02-10
Nonlinear Sciences
Chaotic Dynamics
10 pages, LaTeX, 3 Figures (postscript). Submitted to European Journal of Physics
Scientific paper
10.1088/0143-0807/19/1/011
Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. A well known classical constant of the motion has in the quantum case an ill-defined commutator with the Hamiltonian. It is shown how this problem can be solved. A geometric picture is given revealing why levels of a separable system cross. It is shown that the repulsions found by Ayant and Arvieu are computational effects and that the method used by Traiber et al. is related to the present picture which explains the crossings they find. An asymptotic formula for the energy-levels is derived and it is found that the statistical quantities of the spectrum P(s) and \Delta(L) have the form expected for an integrable system.
Ruijgrok Th. W.
Zon Ramses van
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