Absorbing boundary conditions on a hypersurface for the Schrödinger equation in a half-space Original Research Article

Transparent boundary conditions for the Schrödinger equation iϖtu + Δu = 0 are deduced from the solution of the Cauchy problem set in the whole space. They are established at the hypersurface {xn = 0}. Approximating the symbol of these conditions by means of rational fractions, and introducing auxiliary functions at the boundary, local absorbing conditions are derived. Then, expressing them without surfacic functions, the link between the two kinds of conditions is made.