Separability and Dynamical Symmetry of Quantum Dots
arXiv:1308.3035 · doi:10.1016/j.aop.2013.11.004
Abstract
The separability and Runge-Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonović 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.
32 pages, many figures
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Cited by in corpus (8)
- Hidden Symmetries of Dynamics in Classical and Quantum Physics
- Killing tensors and canonical geometry
- Conformal Killing Tensors and covariant Hamiltonian Dynamics
- Magnetic alteration of entanglement in two-electron quantum dots
- On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields
- On rotationally invariant integrable and superintegrable classical systems in magnetic fields with non-subgroup type integrals
- New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases
- Integrable systems in magnetic fields: the generalized parabolic cylindrical case