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Accurate Molecular Description of a 3-Electron Quantum Dot

The quantum states of 3 interacting, spin-polarized electrons in a parabolic quantum dot in a magnetic field are treated by considering the electron system as a vibrating and rotating molecule. Numerical evidence is presented to show that this picture provides a good qualitative description of the ground state. The electron states are approximated by antisymmetrized molecular rotational-vibrational states. This treatment reproduces the known magic numbers of the 3-electron spin-polarized system and gives the ground-state energy in terms of simple analytic formulas. At large angular momentum, the analytic results agree with the results of numerical diagonalizations to better than one part in 104.