In this paper the scattering of a non-relativistic particle on a semi-infinite crystal is analyzed using the method of the Riemann-Hilbert Problem for analytic functions. We proceed in the framework of the limiting absorption principle. Our formulas allow to find the scattered field at any point of the crystal. In particular, we obtain an explicit formula for the reflection coefficient off the crystal. We discuss the limiting cases of the strong and weak potentials. For compactly supported potentials we present a general result regarding a relation between the reflection and transmission coefficients.
