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arXiv · 1308.3035

Separability and Dynamical Symmetry of Quantum Dots

P. -M. Zhang·L. -P. Zou·P. A. Horvathy·G. W. Gibbons
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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.

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P. -M. Zhang, L. -P. Zou, P. A. Horvathy, G. W. Gibbons. 2013-08-14. Separability and Dynamical Symmetry of Quantum Dots. https://doi.org/10.1016/j.aop.2013.11.004

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