平面上的代数量子哈密顿
Algebraic quantum Hamiltonians on the plane
摘要：
我们考虑二阶微分算子$P$的多项式系数保持向量空间$V_k$的次数不大于$k$。我们假设与$P$的符号相关联的度量是平坦的，并且运算符$P$是潜在的。在两个独立变量的情况下，我们得到了一些分类结果，并找到了椭圆$A_2$和$G_2$ Calogero-Moser哈密顿算子和椭圆Inosemtsev模型的多项式形式。
英文摘要：
We consider second order differential operators $P$ with polynomial coefficients that preserve the vector space $V_k$ of polynomials of degrees not greater then $k$. We assume that the metric associated with the symbol of $P$ is flat and that the operator $P$ is potential. In the case of two independent variables we obtain some classification results and find polynomial forms for the elliptic $A_2$ and $G_2$ Calogero-Moser Hamiltonians and for the elliptic Inosemtsev model.
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