Exact Heisenberg operator solutions for multi-particle quantum mechanics
Quantum Physics
2014-11-18 v1 Other Condensed Matter
High Energy Physics - Theory
Mathematical Physics
Classical Analysis and ODEs
math.MP
Exactly Solvable and Integrable Systems
Abstract
Exact Heisenberg operator solutions for independent `sinusoidal coordinates' as many as the degree of freedom are derived for typical exactly solvable multi-particle quantum mechanical systems, the Calogero systems based on any root system. These Heisenberg operator solutions also present the explicit forms of the annihilation-creation operators for various quanta in the interacting multi-particle systems. At the same time they can be interpreted as multi-variable generalisation of the three term recursion relations for multi-variable orthogonal polynomials constituting the eigenfunctions.
Keywords
Cite
@article{arxiv.0706.0768,
title = {Exact Heisenberg operator solutions for multi-particle quantum mechanics},
author = {Satoru Odake and Ryu Sasaki},
journal= {arXiv preprint arXiv:0706.0768},
year = {2014}
}