Scattering characteristics of a diffraction problem on a wedge and on a screen

Explicit formulae for wave operators are given and the completeness of the operators is established for a class of boundary conditions. It ia shown that modified (taking the reflection into account) scattering matrix is a unitary operator with a pure point spectrum. Ordinary $S$-matrix is a unitary operator for a screen. Under the Dirichlet (Neumann) boundary condition $S$-matrix is diagonalized explicitly. The simple absolutely continuous spectrum of $S$-matrix contains a lower (upper) semicircumference.