Akademik Veri Yönetim Sistemi
PHYSICAL REVIEW B, cilt.72, sa.16, 2005 (SCI-Expanded)
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot and subjected to an external uniform magnetic field have been calculated by using a variational method based on a direct construction of trial wave functions from the quasi-exact analytic solution of the problem. This nonperturbative method not only allows us to obtain accurate results, valid for the whole range of both spatial confinement length and the strength of the magnetic field, but also enables us to compare its analytical results with those previously found in the literature, which are crucial because of testing its reliability. It is found that our results are in excellent agreement with those of the particular exact analytical results, and are convincingly better than those found by using the uncorrelated Landau level wave functions. In fact, the approximate analytical scheme proposed here covers these results in a self-consistent manner; in other words, those can be easily reproduced by just attributing some certain values to the parameters included in the formulation. Furthermore, we have compared our results for the ground-state energy with those obtained by using conventional techniques such as Hartree, Hartree-Fock, exact diagonalization, and quantum Monte Carlo methods. We show that, in addition to its satisfactory internal consistency, our approach yields significant improvement over the Hartree, Hartree-Fock, exact diagonalization treatments, and its results are in agreement with those of the Monte Carlo analysis. Therefore, the approach and its results proposed here would be more helpful to discuss the size dependent properties of low-lying energy levels of two-dimensional parabolic quantum dots with two and specifically several electrons.