On effects of non-Euclidean geometry in quantum theory

Theory of scattering of a quantum-mechanical particle on a cosmic string is developed. S-matrix and scattering amplitude are determined as functions of the flux and the tension of the string. We reveal that, in the case of the nonvanishing tension, the high-frequency limit of the differential scattering cross section does not coincide with the differential cross section for scattering of a classical pointlike particle on a string.