Oscillating properties of a two-electron quantum dot in the presence of a magnetic field

We study the system consisted of two electrons in a quantum dot with a three-dimensional harmonic confinement potential under the effect of a magnetic field. Specifically, two different confinement conditions are considered, one isotropic three-dimensional and the other anisotropic quasi-two-dimensional. Singlet and triplet lowest states properties as the energy, the exchange coupling, the two-electron density function and the spatial spreading of the two electrons in terms of the variance along the x-direction are analysed. In this study we employ the full configuration interaction method with Cartesian anisotropic Gaussian-type orbitals as basis set. These functions allow to explore the confining characteristics of a potential due to their flexibility of using different exponents for each direction in space. The convergence of the results, depending on the size of the set of basic functions, is examined and the oscillations of different physical quantities, concerning the singlet and triplet states, as a function of the magnetic field are discussed.