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

## Abstract

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.

- Authors:

- Indian Institute of Science, Bangalore 560012 (India)
- Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085 (India)

- Publication Date:

- OSTI Identifier:
- 22617371

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 372; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; CHAOS THEORY; DIRICHLET PROBLEM; EXACT SOLUTIONS; INTEGRAL CALCULUS

### Citation Formats

```
Manjunath, Naren, Samajdar, Rhine, and Jain, Sudhir R., E-mail: srjain@barc.gov.in.
```*A difference-equation formalism for the nodal domains of separable billiards*. United States: N. p., 2016.
Web. doi:10.1016/J.AOP.2016.04.014.

```
Manjunath, Naren, Samajdar, Rhine, & Jain, Sudhir R., E-mail: srjain@barc.gov.in.
```*A difference-equation formalism for the nodal domains of separable billiards*. United States. doi:10.1016/J.AOP.2016.04.014.

```
Manjunath, Naren, Samajdar, Rhine, and Jain, Sudhir R., E-mail: srjain@barc.gov.in. Thu .
"A difference-equation formalism for the nodal domains of separable billiards". United States.
doi:10.1016/J.AOP.2016.04.014.
```

```
@article{osti_22617371,
```

title = {A difference-equation formalism for the nodal domains of separable billiards},

author = {Manjunath, Naren and Samajdar, Rhine and Jain, Sudhir R., E-mail: srjain@barc.gov.in},

abstractNote = {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 = {10.1016/J.AOP.2016.04.014},

journal = {Annals of Physics},

number = ,

volume = 372,

place = {United States},

year = {Thu Sep 15 00:00:00 EDT 2016},

month = {Thu Sep 15 00:00:00 EDT 2016}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.