Monodromy-free Schrödinger operators with quadratically increasing potentials
Monodromy-free Schrödinger operators with quadratically increasing potentials
复制标题
具有二次增加势的无单性薛定谔算子
DOI：
10.1007/bf02557204
复制
发表时间：
1999
影响因子：
1
通讯作者：
A. Oblomkov
中科院分区：
文献类型：
--
作者：
A. Oblomkov
我们考虑具有二次递增有理势的一维无单调Schrödinger算子。证明了所有这些算子都可以通过有限次有理达布变换从算子-∂2 + x2中得到。用埃尔米特多项式给出了相应势的显式表达式。
We consider one-dimensional monodromy-free Schrödinger operators with quadratically increasing rational potentials. It is shown that all these operators can be obtained from the operator -∂2 + x2 by finitely many rational Darboux transformations. An explicit expression is found for the corresponding potentials in terms of Hermite polynomials.