Classical and quantum-wedge billiards

The wedge billiard in the plane is considered both quantum mechanically and classically. In the quantum domain, two classes of solutions emerge depend ing on the wedge angle theta (0). In the first class, corresponding to vert ex angles pi theta (0) = s greater than or equal to 2 and integer, eigenfun ctions are real-analytic in the closed domain of the wedge. Incident and re flected waves on the vertex are shown to have equal and opposite current de nsities. In the classical domain, it is established that only at these angl es does a trajectory on the vertex of the wedge nonsingularly retroreflect from the vertex (i.e., reflects from the vertex). Furthermore, the billiard is integrable at these vertex angles. In the second class, pi theta (0) no t equal s, eigenfunctions are irregular at the origin and the related class ical motion is nonintegrable. Application of these results to other areas o f technology is noted. (C) 2001 Elsevier Science B.V. All rights reserved.