  We consider the time discretization based on Lie-Trotter splitting, for the
nonlinear Schrodinger equation, in the semi-classical limit, with initial data
under the form of WKB states. We show that both the exact and the numerical
solutions keep a WKB structure, on a time interval independent of the Planck
constant. We prove error estimates, which show that the quadratic observables
can be computed with a time step independent of the Planck constant. The
functional framework is based on time-dependent analytic spaces, in order to
overcome a previously encountered loss of regularity phenomenon.
