The Quantum-Classical Correspondence in Polygonal Billiards

Details The Quantum-Classical Correspondence in Polygonal Billiards The Quantum-Classical Correspondence in Polygonal Billiards

2000-08-18

arxiv.org/abs/nlin/0008024v2

Nonlinear Sciences

Chaotic Dynamics

8 pages, 9 figures (in reduced quality), to appear in PRE

Scientific paper

10.1103/PhysRevE.64.026212

We show that wave functions in planar rational polygonal billiards (all angles rationally related to Pi) can be expanded in a basis of quasi-stationary and spatially regular states. Unlike the energy eigenstates, these states are directly related to the classical invariant surfaces in the semiclassical limit. This is illustrated for the barrier billiard. We expect that these states are also present in integrable billiards with point scatterers or magnetic flux lines.

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