Solutions of one-dimensional Schrödinger equation with hardy-type potential. The $S$-matrix formalism

A general method is developed for investigating the solutions of the scattering problem for the one-dimensional SchrSdinger equation with Hardy potential. The method uses the formalism of stationary scattering theory. In the quasiclassical and wave (anticlassical) approximations, calculations are made of the amplitude of reflection of particles from a potential with Hardy function describing Bragg scattering of shortwavelength radiation on static elastic distortions of dislocation type in a crystal lattice.