On the Eigenstates of the Elliptic Calogero–Moser Model
On the Eigenstates of the Elliptic Calogero–Moser Model
复制标题
椭圆Calogero-Moser模型的本征态
DOI：
10.1023/a:1011073115698
复制
发表时间：
2000
影响因子：
1.2
通讯作者：
K. Takemura
中科院分区：
文献类型：
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作者：
K. Takemura
已知三角Calogero-Sutherland模型是由椭圆型Calogero-Moser模型的三角极限（τ→√−1∞）得到的，其中（1,τ）是椭圆函数的一个基本周期。我们证明了对于Calogero-Sutherland模型的所有平方可积的特征态和特征值，如果exp（2π√- 1τ）足够小，则椭圆型Calogero-Moser模型的哈密顿量存在平方可积的特征态和特征值，并且收敛于2粒子和耦合常数为正整数的情况下和3粒子和1 =1的情况下Calogero-Sutherland模型的特征态和特征值。换句话说，我们证明了关于参数exp（2π√- 1τ）的正则扰动。在一些假设条件下，我们给出了n粒子和正整数情况下的类似结果。
It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (τ→√−1∞) of the elliptic Calogero–Moser model, where (1, τ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2π√−1τ) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constantlis positive integer cases and the 3-particle andl=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2π√−1τ). With some assumptions, we show analogous results forN-particle andlis positive integer cases.