发表机构
Institute for Physical Research; Nuclear Physics Institute of the Czech Academy of Sciences; University of Hradec Králové（物理研究所; 捷克科学院核物理研究所; 赫拉德茨克拉洛韦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构造了一个幂-刘维尔厄米轨道，将奇异六次振荡器等四种势的谱量化关联，实现了精确厄米可解性、能量量化等性质的统一。
AI 中文摘要
有限厄米双合流-休恩层级中的奇异六次振荡器生成了一个精确的四成员幂-刘维尔厄米轨道。利用刘维尔振幅的幂坐标变换，可将层级成员N=4映射到四条半直线薛定谔谱图，同时在能量耦合重新参数化下保持物理正则-隐性朗斯基零集不变。其中两条谱图是此前研究过的x^(2/3)势与反平方根条件可积势；该轨道将这一已知的幂对偶对与奇异六次、线性加二次谱图一同嵌入。在选定的物理切片上，五次辅助相容性障碍恒为零，而变换后的弗罗贝尼乌斯指数重现了已发表的两个分数幂离心系数。共同端点条件为六次振荡器产生了精确的离散四次斯特姆本征耦合序列。独立的双侧射击法证实了代表性本征耦合与节点数。匹配的大作用量分析进一步导出了主朗格作用量内的首个匹配端点修正，并改进了马斯洛移位的有效能级近似。该构造因此在单一谱轨道内连接了精确厄米可解性、能量量化、耦合量化与幂对偶性。
英文摘要
A singular sextic oscillator in the finite-Hermite biconfluent-Heun hierarchy generates an exact four-member power-Liouville Hermite orbit. Power coordinate transformations with the Liouville amplitude map the hierarchy member $N=4$ to four half-line Schrödinger spectral charts while preserving the physical regular-recessive Wronskian zero set under energy-coupling reparametrization. Two charts are the previously studied $x^{2/3}$ and inverse-square-root conditionally integrable potentials; the orbit embeds this known power-dual pair together with the singular sextic and linear-plus-quadratic charts. On the selected physical slice, the degree-five accessory compatibility obstruction vanishes identically, while the transformed Frobenius index reproduces both published fractional-power centrifugal coefficients. The common endpoint condition yields an exact discrete sequence of quartic Sturmian eigencouplings for the sextic oscillator. Independent two-sided shooting confirms representative eigencouplings and node counts. A matched large-action analysis further derives the first matched-endpoint correction within the leading Langer action and improves the Maslov-shifted effective-level approximation. The construction thus connects exact Hermite solvability, energy quantization, coupling quantization, and power duality within a single spectral orbit.
Comments24 pages, 1 figure
