Unified Supersymmetric Description of Shape-Invariant Potentials within and beyond the Natanzon Class
Unified Supersymmetric Description of Shape-Invariant Potentials within and beyond the Natanzon Class
复制标题
Natanzon 类内外形状不变势的统一超对称描述
DOI：
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发表时间：
2024
期刊：
影响因子：
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通讯作者：
G. Lévai
中科院分区：
文献类型：
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作者：
T. Soltesz;Levente Ferenc Pethő;G. Lévai
在一个采用六参数函数的形式下讨论了超对称量子力学的变换，由此构造了超势和超对称对称势V−(X)和V+(X)的一般形式。通过参数的具体选择，V−(X)和V+(X)与PI类势的一般形式及其有理扩张形式相匹配。参数的选择还确定了四种可能的超对称变换中的哪一种，i=1，…4是有效的。在这一一般性讨论之后，公式被指定为这类势的三个成员，即SCARF I、SCARF II和广义Pöschl-Teller势。由于定义域的不同及其对边界条件的影响，对于这三个势，结果是相当不同的，而数学形式和通过SUSYQM变换相互关联的势的网络在很大程度上仍然是共同的。总框架允许对早先孤立的调查结果进行统一和一致的解释。它还有助于将结果与进一步的潜在类联系起来，并将它们置于准确可解的势的动物园中的更一般的上下文中。
The transformations of supersymmetric quantum mechanics are discussed within a formalism that employs a six-parameter function, from which the superpotential and the supersymmetric partner potentials V−(x) and V+(x) are constructed in a general form. By specific choice of the parameters, V−(x) and V+(x) are matched with the general form of PI class potentials and their rationally extended versions. The choice of the parameters also determines which of the four possible SUSY transformations Ti, i=1,…4 is in effect. After this general discussion, the formulae are specified to the three members of this potential class, the Scarf I, Scarf II and generalized Pöschl–Teller potentials. Due to the different domains of definition and their consequences on the boundary conditions, the results turn out to be rather diverse for the three potentials, while the mathematical formalism and the network of the potentials interconnected by the SUSYQM transformations still remains common to a large extent. The general framework allows a unified and consistent interpretation of earlier isolated findings. It also helps to connect the results to further potential classes and to place them into a more general context within the zoo of exactly solvable potentials.