کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8202116 | 1529860 | 2014 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A nodal domain theorem for integrable billiards in two dimensions
ترجمه فارسی عنوان
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موضوعات مرتبط
مهندسی و علوم پایه
فیزیک و نجوم
فیزیک و نجوم (عمومی)
چکیده انگلیسی
Eigenfunctions of integrable planar billiards are studied - in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a family are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Physics - Volume 351, December 2014, Pages 1-12
Journal: Annals of Physics - Volume 351, December 2014, Pages 1-12
نویسندگان
Rhine Samajdar, Sudhir R. Jain,