Separability and Dynamical Symmetry of Quantum Dots
High Energy Physics - Theory
2015-06-16 v3 Mathematical Physics
math.MP
Quantum Physics
Abstract
The separability and Runge-Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonovi\'c et al. [1], is traced back to that of the perturbed Kepler problem. A large class of axially symmetric perturbing potentials which allow for separation in parabolic coordinates can easily be found. Apart of the 2:1 anisotropic harmonic trapping potential considered in [1], they include a constant electric field parallel to the magnetic field (Stark effect), the ring-shaped Hartmann potential, etc. The harmonic case is studied in detail.
Cite
@article{arxiv.1308.3035,
title = {Separability and Dynamical Symmetry of Quantum Dots},
author = {P. -M. Zhang and L. -P. Zou and P. A. Horvathy and G. W. Gibbons},
journal= {arXiv preprint arXiv:1308.3035},
year = {2015}
}
Comments
32 pages, many figures