  We study the Schr\"odinger equation which comes from the paraxial
approximation of the Helmholtz equation in the case where the direction of
propagation is tilted with respect to the boundary of the domain. This model
has been proposed in (Doumic, Golse, Sentis, CRAS, 2003). Our primary interest
here is in the boundary conditions successively in a half-plane, then in a
quadrant of R2. The half-plane problem has been used in (Doumic, Duboc, Golse,
Sentis, JCP, to appear) to build a numerical method, which has been introduced
in the HERA plateform of CEA.
