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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 Schrö dinger equation (Helmholtz
equation) is separable admit trivial expressions for the number
of domains. Here, we discover that for all separable and nonseparable
integrable billiards, ν satisfies certain difference equations.
This has been possible because the eigenfunctions can be
classified in families labelled by the same value ofm mod kn, 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
- 2014-10-06 20:57:54下载
- 积分：1
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tuihuo-suanfa
模拟退火应用算法 可以用于一部分信号的处理(Application of simulated annealing algorithm)
- 2013-09-24 21:05:33下载
- 积分：1
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filter_0
实现spwm谐波消除方法滤波器的设计模型搭建。(To achieve the spwm harmonic elimination filter design and the model structures.)
- 2013-04-14 17:42:33下载
- 积分：1
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active
振动理论中的主动控制程序，对于振动方面的学习有一定的帮助。(The active control of vibration theory program, the vibration aspects of learning have some help.)
- 2014-02-25 14:36:13下载
- 积分：1
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yc
说明： 遗传寻优算法(Genetic optimization algorithm)
- 2019-01-05 15:55:14下载
- 积分：1
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Matlab-mathematical-modeling
matlab 数学建模与应用 适用于已经入门的matlab用户(matlab mathematical modeling and application has been started for matlab users)
- 2011-11-11 21:10:40下载
- 积分：1
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PF_codes
非线性滤波算法中的粒子滤波，用于目标定位与跟踪。(Nonlinear filtering algorithm in the particle filter for target tracking.)
- 2010-05-11 20:51:08下载
- 积分：1
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chaotic-simulink
关于混沌系统同步的滑模变结构仿真，采用s函数，很有意义。(Synchronization of chaotic systems on sliding mode simulation, using the s function, it makes sense.)
- 2011-07-01 12:10:30下载
- 积分：1
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1
说明： M-file to calculate and plot the velocity and
- 2009-11-05 02:45:11下载
- 积分：1
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p
说明： 现代数字信号处理的经典功率谱估计方法例程,有详细备注解释(A classic of modern digital signal processing power spectrum estimation routines, contains a detailed explanation Remarks)
- 2009-11-17 13:11:10下载
- 积分：1
