论文标题
在某些条件解决的量子力学问题上
On some conditionally solvable quantum-mechanical problems
论文作者
论文摘要
我们分析了两个有条件解决的量子力学模型：一维六振荡器和一个扰动的库仑问题。两者都导致扩展系数的三届复发关系。我们显示了其确切特征值的分布图，并通过从变化计算中添加精确的特征值。我们讨论了这种分布的对称性。我们还评论了一些研究人员对确切特征值和特征功能的错误解释，这导致了允许的回旋频率和野外强度的预测。
We analyze two conditionally solvable quantum-mechanical models: a one-dimensional sextic oscillator and a perturbed Coulomb problem. Both lead to a three-term recurrence relation for the expansion coefficients. We show diagrams of the distribution of their exact eigenvalues with the addition of accurate ones from variational calculations. We discuss the symmetry of such distributions. We also comment on the wrong interpretation of the exact eigenvalues and eigenfunctions by some researchers that has led to the prediction of allowed cyclotron frequencies and field intensities.
