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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}
}
R2 v1 2026-06-21T08:35:36.579Z