New Formulas for the Eigenfunctions of the Two-Particle Difference Calogero-Moser System

被引：1

作者：

Gaillard, Pierre ^{[1
]}

Matveev, Vladimir ^{[1
]}

机构：

[1] Univ Bourgogne, Inst Math Bourgogne, F-21078 Dijon, France

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2009年 / 89卷 / 01期

关键词：

Casorati determinants; deformations; Darboux-Poschl-Teller equation; difference Calogero-Moser systems; difference Darboux transformations; DARBOUX TRANSFORMATION;

D O I：

10.1007/s11005-009-0315-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present a new proof of the integrability of the DDPT-I equation. The DDPT-I equation represents a functional-difference deformation of the well-known Darboux-Poschl-Teller equation. The proof is based on some formula for special Casorati determinants established in the paper. This formula provides some new representation for the DDPT-I potentials and for the general solution for the DDPT-I equation. It allows also a very easy computation of the action of the difference KdV flow on the DDPT-I initial data. In other words we obtain the new formulas for the eigenfunctions of the Hamiltonians of the two-particle difference BC (1) Calogero-Moser system also known as quantum relativistic Calogero-Moser, (QRCM), system.

引用

页码：1 / 12

页数：12

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