Solution of the eigenvalue problem for two-dimensional modulated billiards using a coordinate transformation

✍ Scribed by J.A. Méndez-Bermúdez; G.A. Luna-Acosta; F.M. Izrailev; R. Aguilar-Sánchez

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 285 KB
• Volume: 10
• Category: Article
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2004.05.001

✦ Synopsis

We propose a method to solve the eigenvalue problem for a generic two-dimensional modulated billiard by using a coordinate transformation. The transformation allows us to incorporate the effects of the billiard's boundaries into an effective potential, rendering the one particle motion in the two-dimensional billiard equivalent to that of two interacting particles in a one-dimensional geometry. We give the expressions for the Hamiltonian matrix elements for the cases of periodic and closed billiards.