为扩展类截断Calogero-Sutherland模型生成支持零能量可归一化态的QES势
Generating QES potentials supporting zero energy normalizable states for an extended class of truncated Calogero Sutherland model
AI总结：
本研究针对有理扩展多体截断Calogero-Sutherland模型，基于带$so(2,1)$结构的势群方法与点正则变换，得到三类同本征值的准精确可解势，证明其存在零能量可归一化束缚态。
摘要：
受近期寻找其底层薛定谔方程可解的生成势的研究兴趣启发，我们在近期工作中报道了若干种零能量态成为束缚态的情形，这取决于定义势的耦合常数的特定限制条件。在这方面，我们给出证据表明，对应于有理扩展多体截断Calogero-Sutherland（TCS）模型的一类准精确可解（QES）势系统，存在正则的零能量可归一化解。我们的方法基于使用具有底层$so(2,1)$结构的标准势群方法，该方法利用点正则变换，得到三类具有相同本征值的不同势，而它们的共同性质需通过相关波函数的计算来验证。我们通过适当限制耦合参数，分别处理了这些情形。
英文摘要：
Motivated by recent interest in the search for generating potentials for which the underlying Schrödinger equation is solvable, we report in the recent work several situations when a zero-energy state becomes bound depending on certain restrictions on the coupling constants that define the potential. In this regard, we present evidence of the existence of regular zero-energy normalizable solutions for a system of quasi-exactly solvable (QES) potentials that correspond to the rationally extended many-body truncated Calogero-Sutherland (TCS) model. Our procedure is based upon the use of the standard potential group approach with an underlying $so(2, 1)$ structure that utilizes a point canonical transformation with three distinct types of potentials emerging having the same eigenvalues while their common properties are subjected to the evaluation of the relevant wave functions. These cases are treated individually by suitably restricting the coupling parameters.
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