可解势的相互关系

A. Gangopadhyaya, P. Panigrahi, U. Sukhatme
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引用次数: 13

摘要

已知非相对论量子力学中可解的Natanzon势可以分为两个不相交的类,这取决于Schr\ odinger方程是否可以简化为超几何方程或合流超几何方程。每个类中的所有势都通过点正则变换连接起来。我们用适当的极限程序和参数的重新定义建立了两类之间的联系,从而将所有已知的可解势相互联系起来。
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Inter-Relations of Solvable Potentials
Solvable Natanzon potentials in nonrelativistic quantum mechanics are known to group into two disjoint classes depending on whether the Schr\"odinger equation can be reduced to a hypergeometric or a confluent hypergeometric equation. All the potentials within each class are connected via point canonical transformations. We establish a connection between the two classes with appropriate limiting procedures and redefinition of parameters, thereby inter-relating all known solvable potentials.
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