超对称缠绕关系的三维解与等谱Hamilton算子对
Three-Dimensional Solutions of Supersymmetrical Intertwining Relations and Pairs of Isospectral Hamiltonians
摘要：
利用具有非退化常数度量的二阶超荷类，建立了三维薛定谔算子的超对称缠绕关系的一般解。该解决方案包括几个模型与任意参数。我们只对不服从分离变量的量子系统感兴趣，也就是说，它不能被简化为低维问题。所有构造的哈密顿算子都是部分可积的--它们中的每一个都与动量为四阶的对称算子交换。同样的模型也可以被认为是复杂的参数值，导致一类非厄米等谱哈密顿。
英文摘要：
The general solution of SUSY intertwining relations for three-dimensional Schrödinger operators is built using the class of second order supercharges with nondegenerate constant metric. This solution includes several models with arbitrary parameters. We are interested only in quantum systems which are not amenable to separation of variables, i.e. can not be reduced to lower dimensional problems. All constructed Hamiltonians are partially integrable - each of them commutes with a symmetry operator of fourth order in momenta. The same models can be considered also for complex values of parameters leading to a class of non-Hermitian isospectral Hamiltonians.
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