Eigenvalues for p^2+x^2(ix)^\epsilon

This file contains a set of eigenvalues obtained by solving the eigenvalue problem associated with the differential equation $-\frac{\partial^2 \psi}{\partial x^2}+x^2(i x)^\epsilon\psi=E\psi$. The method of solution is numerical in nature using Mathematica 9's built in NDSolve function with a 9th order adaptive Runge-Kutta method and a standardized shooting algorithm. All eigenvalues are quoted to 6 places and have been calculated to higher precision in order to ensure 6 valid places. This problem was oringally solved and published under: Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry by Carl M Bender and Stefan Boettcher [Phys.Rev.Lett. 80 (1998) 5243-5246]. This dataset demonstrates independent reproduction of the original results and makes the data underlying the figures in the paper available to those who wish to check their own results. Further eigenvalues and supporting information to follow in this dataset [DWH - 14/2/2013].

本文件包含一组通过求解与微分方程 $-frac{partial^2 psi}{partial x^2}+x^2(ix)^epsilonpsi=Epsi$ 相关的特征值问题得到的特征值。本求解方法采用数值方法，使用Mathematica 9的内置NDSolve函数，搭配九阶自适应龙格-库塔（Runge-Kutta）方法与标准化打靶算法。所有特征值均保留六位有效数字，且为确保这六位有效数字的准确性，计算时采用了更高的精度。该问题最初由Carl M Bender与Stefan Boettcher在论文《具有PT对称（PT Symmetry）的非厄米哈密顿量的实谱》中求解并发表，相关文献见于[Phys.Rev.Lett. 80 (1998) 5243-5246]。本数据集实现了原始结果的独立复现，并可为希望验证自有结果的研究者提供该论文配图所依托的原始数据。本数据集后续将补充更多特征值及辅助信息 [DWH - 2013年2月14日]。