A difference-equation formalism for the nodal domains of separable billiards

Journal Article · Thu Sep 15 00:00:00 EDT 2016 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2016.04.014· OSTI ID:22617371

Manjunath, Naren; Samajdar, Rhine ^[1]

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1. Indian Institute of Science, Bangalore 560012 (India)

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.

• OSTI ID: 22617371
• Journal Information: Annals of Physics, Vol. 372; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
CHAOS THEORY
DIRICHLET PROBLEM
EXACT SOLUTIONS
INTEGRAL CALCULUS