We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coefficients of the power series that, under suitable truncation, yields exact analytical eigenvalues and eigenfunctions for particular values of a model parameter. From these solutions some researchers have derived a variety of predictions like allowed angular frequencies, allowed field intensities and the like. We also solve the eigenvalue equation numerically by means of the variational Ritz method and compare the resulting eigenvalues with those provided by the truncation condition. In this way we prove that those physical predictions are merely artifacts of the truncation condition.

中文翻译：

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对有条件可解特征值方程的严重误解

我们求解了一个特征值方程，该方程出现在几篇关于各种物理问题的论文中。Frobenius 方法导致幂级数系数的三项递推关系，在适当的截断下，产生模型参数特定值的精确分析特征值和特征函数。从这些解决方案中，一些研究人员得出了各种预测，例如允许的角频率、允许的场强等。我们还通过变分 Ritz 方法对特征值方程进行数值求解，并将得到的特征值与截断条件提供的特征值进行比较。通过这种方式，我们证明了这些物理预测仅仅是截断条件的伪影。