Two-dimensional Coulomb scattering of a quantum particle. The wave functions and Green functions

By assumption, a charged quantum particle moves in the two-dimensional plane of the three-dimensional configuration space and is scattered by the fixed Coulomb center lying in the same plane. The wave function of this particle, the Green function and all radial components of these functions are studied. For the modules of these components the uniform major bounds are derived. The representation of the wave function in terms of the regular radial Coulomb functions and the representation of the scattering amplitude in terms of the partial phase shifts are found. For the Green function and its radial components the integral representations are obtained