Supersymmetry, operator transformations and exactly solvable potentials
Supersymmetry, operator transformations and exactly solvable potentials
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超对称性、算子变换和精确可解势
DOI：
10.1088/0305-4470/22/17/035
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发表时间：
1989
期刊：
影响因子：
--
通讯作者：
A. Wipf
中科院分区：
文献类型：
--
作者：
Fred Cooper;J. Ginocchio;A. Wipf
利用超对称性和形状不变性，可以用代数方法求解一大类势函数。作者应用算子变换（f变换），这些代数可解的问题，以获得一个更大的类的可解的潜力-Natanzon类的潜力，这是不是形状不变的。使用算符变换从旧势中找到新势的重要条件（与超对称性无关）是所得到的薛定谔方程具有不依赖于状态的势。作为f变换的一个特例，他们重新推导了先前已知的三维谐振子、氢原子和莫尔斯势之间的联系。他们还讨论了缺乏交换性的超对称性和f变换。
A large class of potentials can be solved algebraically by using supersymmetry and shape invariance. The authors apply operator transformations (f transformations) to these algebraically solvable problems to obtain a larger class of solvable potentials-the Natanzon class of potentials which are not shape invariant. The important condition (which is independent of supersymmetry) for finding new potentials from old ones using operator transformations is that the resulting Schrodinger equation has a potential which does not depend on the state. As a special case of the f transformation they rederive the previously known connection between the 3D harmonic oscillator, the hydrogen atom and the Morse potential. They also discuss the lack of commutivity of SUSY and the f transformations.