Generalized Lamé functions. II. Hyperbolic and trigonometric specializations
Generalized Lamé functions. II. Hyperbolic and trigonometric specializations
复制标题
广义拉梅函数 II。
DOI：
10.1063/1.532823
复制
发表时间：
1999
影响因子：
1.3
通讯作者：
S. Ruijsenaars
中科院分区：
文献类型：
--
作者：
S. Ruijsenaars
在第一部分[J.Math.Phys.40，1595（1999）]中，我们研究了定义具有椭圆相互作用的两粒子相对论Calogero-Moser系统的量子动力学的本征函数。在本文中，我们考虑同一系统的双曲和三角相互作用。在这些特殊的制度的特征函数表明，承认一个基本的表示，这是更明确的比“零表示”的第一部分。特别是，新的表示可以用来证明双曲本征函数可以被选择为在互换位置和动量变量（自对偶）下对称。在三角的情况下，对偶性质推导，也得到了几个正交性和完备性的结果。
In Part I [J. Math. Phys. 40, 1595 (1999)] we studied eigenfunctions of the quantum dynamics that defines the two-particle relativistic Calogero–Moser system with elliptic interaction. In the present paper we consider the same system with hyperbolic and trigonometric interactions. In these special regimes the eigenfunctions are shown to admit an elementary representation that is far more explicit than the “zero representation” of Part I. In particular, the new representation can be exploited to prove that the hyperbolic eigenfunctions can be chosen to be symmetric under interchanging position and momentum variables (self-duality). In the trigonometric case duality properties are derived, too, and several orthogonality and completeness results are obtained.