Exact solution of the Thomas-Fermi two-dimensional N-electron parabolic quantum dot

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23 Scopus citations


The Thomas-Fermi approach is applied to the problem of the two-dimensional parabolic quantum dot. The equation is solved exactly in conjunction with Poisson’s equation for a circularly symmetric parabolic confinement. The solutions depend only on the ratio between the square of the product of the confinement constant and the dielectric constant of the host material and on the number of electrons. Asymptotic solutions for weak and strong confinement were also obtained for the chemical potential, the total energy, and the differential capacitance, reproducing the correct trends. For bounded parabolic potentials, an estimate of the maximal number of electrons that a dot can support is given. Appropiate Gaussian asymptotic behavior for the density is obtained by including a Weizsäcker-type kinetic energy term.

Original languageEnglish (US)
Pages (from-to)4644-4648
Number of pages5
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number8
StatePublished - 1998

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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