The accuracy of the Hartree-Fock approximation for quantum dots

The authors investigate the accuracy of the Hartree-Fock (HF) and Hartree (H) approximations for calculating energies in an N-electron quantum dot. The HF and H energies calculated from an analytically solvable model Hamiltonian are compared to exact energy solutions. The HF and H approximations become less accurate with increasing number of electrons, decreasing magnetic field, increasing dot size and increasing electron-electron interaction strength. The dependence on electron number is contrary to the well known infinite electron gas result.