The constrained-search principle introduced by Levy and Lieb, is proposed as a practical, though conceptually rigorous, link between Density Functional Theory (DFT) and Quantum Monte Carlo (QMC). The resulting numerical protocol realizes in practice the implicit key statement of DFT: 'Given the three dimensional electron density of the ground state of a system of N electrons with external potential v(r) it is possible to find the corresponding 3N-dimensional wavefunction of ground state.' From a numerical point of view, the proposed protocol can be employed to speed up the QMC procedure by employing DFT densities as a pre-selection criterion for the sampling of wavefunctions. (C) 2014 Elsevier B.V. All rights reserved.