Electronic levels of cubic quantum dots

We introduce an efficient variational method to solve the three-dimensional Schrodinger equation for any arbitrary potential V(x, y, z). The method us es a basis set of localized functions which are build up as products of one -dimensional cubic beta -splines. We calculate the energy levels of GaAs/Al GaAs cubic quantum dots and make a comparison with the results from two wel l-known simplification schemes based on a decomposition of the full potenti al problem into three separate one-dimensional problems. We show that the s cheme making a sequential decomposition gives eingenvalues in better agreem ent with the ones obtained variationally, but an exact solution is necessar y when looking for highly precise values.