  This paper is concerned with the numerical analysis of linear and nonlinear
Schr{\"o}dinger equations with analytic potentials. While the regularity of the
potential (and the source term when there is one) automatically conveys to the
solution in the linear cases, this is no longer true in general in the
nonlinear case. We also study the rate of convergence of the planewave
(Fourier) discretization method for computing numerical approximations of the
solution.
