From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics
Abstract
It is shown that planar quantum dynamics can be related to 3-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case the symmetry reduction from degrees of freedom to one degree is presented. A link between two-dimensional (super-integrable) systems and 3-body (super-integrable) systems is revealed. As illustration we present number of examples. We demonstrate that the celebrated Calogero-Wolfes 3-body potential has a unique property: two-dimensional quantum dynamics coincides with 3-body quantum dynamics on the line at ; it is governed by the Tremblay-Turbiner-Winternitz potential for parameter .
Cite
@article{arxiv.1912.05726,
title = {From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics},
author = {Alexander V Turbiner and Willard Miller and M. Adrian Escobar-Ruiz},
journal= {arXiv preprint arXiv:1912.05726},
year = {2021}
}
Comments
13 pages, 24 refs; title modified, several explicit examples added, Abstract and Introduction extended, some statements clarified