标题： 分布式高斯多项式作为q-振荡器本征函数 显示英文标题

标题： Distributed Gaussian polynomials as q-oscillator eigenfunctions

摘要： Karabulut和Sibert（\textit{J. 数学物理}。\textbf{38}（9），4815（1997））从等间距高斯函数的线性组合中构造了一个正交函数集。在本文中，我们证明它们实际上是坐标表示下q-振子的本征函数。我们还重新解释了Macfarlane给出的q-振子坐标表示示例，将其视为相对于一种不寻常的内积定义正交的函数。结果表明，两个q-振子示例中的本征函数都是无限简并的。 显示英文摘要

摘要： Karabulut and Sibert (\textit{J. Math. Phys}. \textbf{38} (9), 4815 (1997)) have constructed an orthogonal set of functions from linear combinations of equally spaced Gaussians. In this paper we show that they are actually eigenfunctions of a q-oscillator in coordinate representation. We also reinterpret the coordinate representation example of q-oscillator given by Macfarlane as the functions orthogonal with respect to an unusual inner product definition. It is shown that the eigenfunctions in both q-oscillator examples are infinitely degenerate.