Quasi-Exact Solvability and the direct approach to invariant subspaces
Quasi-Exact Solvability and the direct approach to invariant subspaces
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准精确可解性和不变子空间的直接方法
DOI：
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发表时间：
2004
期刊：
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通讯作者：
R. Milson
中科院分区：
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作者：
D. Gómez‐Ullate;N. Kamran;R. Milson
我们提出了一种更直接的方法来构造保持多项式子空间的微分算子，而不是基于考虑包络代数的元素。本文用这种方法构造了新的非李代数的精确可解和准精确可解的量子哈密顿量。它也被应用于生成具有多个代数扇区的势。我们讨论了这两种应用的两个例子：我们证明了广义Lame势具有四个代数扇区，并描述了一个非李代数的Morse势的准精确可解变形。
We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of . This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: we show that the generalized Lame potential possesses four algebraic sectors, and describe a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.