Electronic levels of quantum dots: A variational approach

We introduce an efficient variational method to solve the three-dimensional Schrodinger equation for any arbitrary potential V(x,y,z). The method uses a basis set of localized functions which are build up as a product of thre e one-dimensional cubic P-splines. We have analysed the accuracy of such a method by studying some exact 3D potentials: the harmonic oscillator, the h ydrogen atom and the quantum box. Finally, we have calculated energy levels of GaAs/AlGaAs cubic quantum dots and make a comparison with the ones resu lting from two well known simplification schemes, based in a decomposition of the full potential problem into three separated one-dimensional problems . We show that; the scheme making a sequential decomposition gives eingenva lues in better agreement with exact values here obtained variationally.