energy states and exchange energy of coupled double quantum dot in a magnetic field

The ground state energies of two interacting electrons confined in a coupled double quantum dot (dqd) presented in a magnetic field has been calculated by solving the relative hamiltonian using variational and exact diagonalization methods. the singlet-triplet transitions in the angular momentum and spin of the quantum dot ground state had been shown .we have studied the magnetic field versus confining frequency and magnetic field versus potential barrier height phase diagram of dqd .furthermore, we have investigated the dependence of the exchange energy of two electron double quantum dot on the confining frequency, potential height barrier, barrier width and magnetic field strength. the comparisons show that our results are in very good agreement with reported works.