  In this paper we study the application of the Sobolev gradients technique to
the problem of minimizing several Schr\"odinger functionals related to timely
and difficult nonlinear problems in Quantum Mechanics and Nonlinear Optics. We
show that these gradients act as preconditioners over traditional choices of
descent directions in minimization methods and show a computationally
inexpensive way to obtain them using a discrete Fourier basis and a Fast
Fourier Transform. We show that the Sobolev preconditioning provides a great
convergence improvement over traditional techniques for finding solutions with
minimal energy as well as stationary states and suggest a generalization of the
method using arbitrary linear operators.
