A scattering approach to the quantization of Hamiltonians in two dimensions-application to the wedge billiard

Autor:	C Rouvinez, U Smilansky
Rok vydání:	1995
Předmět:	Integrable system Scattering Mathematical analysis General Physics and Astronomy Periodic orbits Semiclassical physics Statistical and Nonlinear Physics Dynamical billiards Wave function Wedge (geometry) Mathematical Physics Mathematics Hamiltonian system
Zdroj:	Journal of Physics A: Mathematical and General. 28:77-104
ISSN:	1361-6447 0305-4470
DOI:	10.1088/0305-4470/28/1/014
Popis:	We extend the scattering approach to quantize general Hamiltonian systems in two dimensions and demonstrate it for the wedge billiard. The resulting energy levels are given by the zeros of a secular equation. The corresponding wavefunctions may also be constructed. We verify analytically that this quantization condition is exact in the case of the integrable wedges. This method has been applied successfully to computing numerically a few thousand levels for various values of the angle. Using these data, we can check the Gutzwiller trace formula and other semiclassical relations involving the scattering matrix and periodic orbits, for which we find excellent agreement.
Databáze:	OpenAIRE
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