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arXiv math-ph/0209013math-phgr-qcmath.MPnlin.SI
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Ermakov-Milne-Pinney方程的非线性超对称（Darboux）协方差

Nonlinear Supersymmetric (Darboux) Covariance of the Ermakov-Milne-Pinney Equation

M. V. Ioffe, H. J. Korsch

备注：
8 pages
发表信息：
Phys.Lett. A311 (2003) 200-205
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摘要：

证明了非线性Ermakov-Milne-Pinney方程$ρ^{\prime\prime}+v(x)ρ=a/ρ^3$在其系数函数的一类变换下服从协方差性质.这个性质是通过使用超对称或达布变换导出的。变换后的方程的通解用原方程的解表示。这些变换和不可约变换的二阶导数被认为是获得链的相互关联的Ermakov-Milne-Pinney方程。研究了束缚态的Lewis不变量和量子数函数的性质。这种结构是由一个简单的例子说明了一个无限的正方形井。

英文摘要：

It is shown that the nonlinear Ermakov-Milne-Pinney equation $ρ^{\prime\prime}+v(x)ρ=a/ρ^3$ obeys the property of covariance under a class of transformations of its coefficient function. This property is derived by using supersymmetric, or Darboux, transformations. The general solution of the transformed equation is expressed in terms of the solution of the original one. Both iterations of these transformations and irreducible transformations of second order in derivatives are considered to obtain the chain of mutually related Ermakov-Milne-Pinney equations. The behaviour of the Lewis invariant and the quantum number function for bound states is investigated. This construction is illustrated by the simple example of an infinite square well.

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