2 INTERACTING ELECTRONS IN A 3-DIMENSIONAL PARABOLIC QUANTUM-DOT - A SIMPLE SOLUTION

We present a simple solution to the problem of two interacting electro ns confined by a three-dimensional parabolic potential. The method rel ies on the diagonalization of the Hamiltonian in reduced Hilbert space . The basis functions are the solutions of the centre-of-mass motion a nd the relative motion of the two particles without Coulomb interactio n. Since the Coulomb interaction only affects the relative motion, the matrix elements of the Hamiltonian are easily evaluated analytically. The numerical diagonalization is readily performed as only a few basi s functions are needed to obtain a good precision on the energy levels : six basis functions ensure a precision better than 0.1% on the groun d-state energy, while three basis functions are enough to obtain a pre cision better than 1%. The results are analysed and compared to previo usly published results. They are also used to evaluate the precision o f a first-order perturbation calculation for the Coulomb interaction a nd an approach based on a 1/r(2) approximate interaction potential for which there exists an analytical solution.