In this work, the [Formula: see text]-Schrödinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of [Formula: see text], and the limiting case as [Formula: see text] is considered. The Rayleigh–Ritz variational method is adopted to the system. The discrete [Formula: see text]-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: [Formula: see text]-harmonic, purely [Formula: see text]-quartic and [Formula: see text]-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.

中文翻译：

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基于离散q-Hermite I多项式的变分法得到q-薛定谔方程的谱

在这项工作中，考虑了具有对称多项式势的 [公式：见正文]-薛定谔方程。对于[公式：见文本]的几个值，获得模型的光谱，并考虑[公式：见文本]的极限情况。系统采用瑞利-里兹变分法。离散的 [公式：见正文]-Hermite I 多项式在此方法中作为基础处理。此外，以下具有大量结果的势作为应用程序：[公式：参见文本]-谐波，纯 [公式：参见文本]-四次和 [公式：参见文本]-四次振荡器。还表明，获得的结果证实了文献中存在的连续情况。