A difference-equation formalism for the nodal domains of separable billiards
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 t...
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| Veröffentlicht in: | Annals of physics 2016-09, Vol.372, p.68-73 |
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| container_end_page | 73 |
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| container_title | Annals of physics |
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| creator | Manjunath, Naren Samajdar, Rhine Jain, Sudhir R. |
| description | 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. |
| doi_str_mv | 10.1016/j.aop.2016.04.014 |
| format | Article |
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| ispartof | Annals of physics, 2016-09, Vol.372, p.68-73 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Billiards BOUNDARY CONDITIONS CHAOS THEORY CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Differential equations DIRICHLET PROBLEM EXACT SOLUTIONS Integrable billiard INTEGRAL CALCULUS Nodal domain Quantum chaos Theoretical physics |
| title | A difference-equation formalism for the nodal domains of separable billiards |
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