任意维的干涉等谱势
Intertwined isospectral potentials in an arbitrary dimension
摘要：
用n维线性缠绕算子L的缠绕方法构造了n维等谱定常势。在欧氏代数生成元中证明了L的微分部分是一个级数。研究了相容性方程的可积性条件，并对n= 2，3，4，5给出了满足这些条件的一类势函数的一般形式.最一般的形式的二维和三维等谱电位被认为是详细的，并展示其层次结构。下面的方法提供了坐标系，其使得可以执行变量分离并将超对称量子力学的已知方法应用于1D系统。它已被证明，在坐标和L的选择有一些替代品增加与$n$，扩大了可用的潜力集。给出了高维扩张的一些显著特征以及所得结果的一些应用。
英文摘要：
The method of intertwining with n-dimensional (nD) linear intertwining operator L is used to construct nD isospectral, stationary potentials. It has been proven that differential part of L is a series in Euclidean algebra generators. Integrability conditions of the consistency equations are investigated and the general form of a class of potentials respecting all these conditions have been specified for each n=2,3,4,5. The most general forms of 2D and 3D isospectral potentials are considered in detail and construction of their hierarchies is exhibited. The followed approach provides coordinate systems which make it possible to perform separation of variables and to apply the known methods of supersymmetric quantum mechanics for 1D systems. It has been shown that in choice of coordinates and L there are a number of alternatives increasing with $n$ that enlarge the set of available potentials. Some salient features of higher dimensional extension as well as some applications of the results are presented.
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