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Title: Separability and dynamical symmetry of Quantum Dots

The separability and Runge–Lenz-type dynamical symmetry of the internal dynamics of certain two-electron Quantum Dots, found by Simonović et al. (2003), are 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 from the 2:1 anisotropic harmonic trapping potential considered in Simonović and Nazmitdinov (2013), 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. -- Highlights: • The separability of Quantum Dots is derived from that of the perturbed Kepler problem. • Harmonic perturbation with 2:1 anisotropy is separable in parabolic coordinates. • The system has a conserved Runge–Lenz type quantity.
Authors:
 [1] ;  [1] ;  [1] ;  [2] ;  [3]
  1. Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou (China)
  2. (France)
  3. Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge (United Kingdom)
Publication Date:
OSTI Identifier:
22233546
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 341; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; AXIAL SYMMETRY; COORDINATES; DISTURBANCES; ELECTRIC FIELDS; ELECTRONS; MAGNETIC FIELDS; OSCILLATORS; PERTURBATION THEORY; POTENTIALS; QUANTUM DOTS; STARK EFFECT