|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
20 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Calogero-Sutherland-Moser Systems, Ruijsenaars-Schneider-van Diejen Systems and Orthogonal Polynomials | | S. Odake
; R. Sasaki
; | | Date: |
14 Dec 2005 | | Journal: | Prog.Theor.Phys. 114 (2006) 1245-1260 | | Subject: | High Energy Physics - Theory; Mathematical Physics | | Abstract: | The equilibrium positions of the multi-particle classical Calogero-Sutherland-Moser (CSM) systems with rational/trigonometric potentials associated with the classical root systems are described by the classical orthogonal polynomials; the Hermite, Laguerre and Jacobi polynomials. The eigenfunctions of the corresponding single-particle quantum CSM systems are also expressed in terms of the same orthogonal polynomials. We show that this interesting property is inherited by the Ruijsenaars-Schneider-van Diejen (RSvD) systems, which are integrable deformation of the CSM systems; the equilibrium positions of the multi-particle classical RSvD systems and the eigenfunctions of the corresponding single-particle quantum RSvD systems are described by the same orthogonal polynomials, the continuous Hahn (special case), Wilson and Askey-Wilson polynomials. They belong to the Askey-scheme of the basic hypergeometric orthogonal polynomials and are deformation of the Hermite, Laguerre and Jacobi polynomials, respectively. The Hamiltonians of these single-particle quantum mechanical systems have two remarkable properties, factorization and shape invariance. | | Source: | arXiv, hep-th/0512155 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER