A Unitary Transformation and Spectrum of a Three-Electron Quantum Dot |

H. Hassanabadi
^{a}, H. Rahimov^{ b}, and H. Ghasem^{ c}^{a}Physics Department, Shahrood University of Technology, P.O. Box 3619995161-316 Shahrood, Iran
^{b}Computer Engineering, Shahrood University of Technology, Shahrood, Iran
^{c}School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran |

Received: December 2, 2010; In final form February 27, 2011 |

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We consider the Hamiltonian of a three-electron quantum dot composed of parabolic confinement plus the Coulomb terms. Instead of using the Jacobi coordinates, we apply a unitary transformation to this system. To avoid the complexity, the Taylor expansion of the effective potential is introduced into the problem and thereby a solution is found for the eigenvalues of the corresponding three-body SchrÃ¶dinger equation in terms of the Wigner parameter. |

DOI: 10.12693/APhysPolA.120.521 PACS numbers: 73.21.La, 73.20.Qt, 71.10.-w |