椭圆型Calogero-Sutherland模型的多重代数
Multiple algebraisations of an elliptic Calogero-Sutherland model
摘要：
最近，Gomez-Ullate等人（1）研究了一个特殊的具有椭圆函数势和外加场的N粒子量子问题。他们已经证明了哈密顿算子保持了有限维的函数空间，因此是准精确可解的（QES）。在本文中，我们证明了其他类型的不变函数空间的存在，这是密切相关的椭圆函数的代数性质。据此，可以构造一系列新的代数本征函数。
英文摘要：
Recently, Gomez-Ullate et al. (1) have studied a particular N-particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that the Hamiltonian operator preserves a finite dimensional space of functions and as such is quasi exactly solvable (QES). In this paper we show that other types of invariant function spaces exist, which are in close relation to the algebraic properties of the elliptic functions. Accordingly, series of new algebraic eigenfunctions can be constructed.
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