Scattering by a hard corrugated wall: An exact solution

We present an exact solution to Schr\"odinger's equation for the scattering of particles by a hard corrugated wall with a triangular corrugation profile. The solution is applied to the problem of scattering of low-energy atoms by a solid surface, and comparisons are made with the recent experimental data for scattering of helium by stepped copper surfaces. We also give a discussion of the convergence properties of the solution and a detailed comparison with the numerical method of Garcia and Cabrera.