The ground state of two-electron quantum dot in a magnetic field: the 1/N expansion method

The ground-state properties of a two-dimensional quantum-dot are studied. We have used the shifted 1/N expansion method to solve the relative part of the Hamiltonian of two electrons confined in a quantum dot in the presence of an applied uniform magnetic field. The spin singlet-triplet transition in the ground state of the QD is shown. We have also displayed the singlet-triplet energy gap against the strength of the magnetic field for a two electron quantum dot. Based on comparisons, the eigenenergies obtained by the 1/N shifted method are in excellent agreement with exact numerical diagonalization and variational methods.