二维Helmholtz方程在超圆边界上Dirichlet或Neumann条件下本征谱的半经验公式
A semi-empirical formula for the eigenspectrum of the 2-dimensional Helmholtz equation with Dirichlet or Neumann condition on a supercircular boundary
摘要：
\cite{chak} Chakraborty等人在最近的一篇论文中提出了一种求解二维齐次Helmholtz方程在超圆边界上Dirichlet条件的摄动方法。本文对同一问题给出了一个单参数（超圆指数或指数）半经验公式。同样的公式现在也适用于Neumann型边界条件。通过比较几个低能级的本征值与相应的数值估计，对公式进行了检验。可以看出，该公式给出的结果具有显着的精度为超圆指数的范围很广。
英文摘要：
In a recent paper \cite{chak} Chakraborty et al have put forward a perturbative formulation for solving the 2 dimensional homogeneous Helmholtz equation with the Dirichlet condition on a supercircular boundary. In this note a single parameter (supercircular exponent or exponent) semi-empirical formula, giving the eigenspectrum, is presented for the same problem. The same formula now is also applicable for the Neumann type boundary condition. The formula is put to test by comparing the obtained eigenvalues for several low lying states with their corresponding numerical estimates. It is seen that the formula gives results with a remarkable accuracy for a wide range of the supercircular exponent.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
