The paper critically examines the details of the corresponding theoretical problem of particle scattering in non-relativistic quantum mechanics. The discussion proceeds in two directions: one - the correctness of physical and mathematical interpretations of individual details of the scattering problem; second - checking the correctness of mathematical methods used in specific mathematical calculations. Details of the scattering problem are pointed out, whose existing interpretations contradict the basic principles of quantum mechanics. A detail of mathematical calculations is also pointed out, contradicting the principle of correct calculation and leads the corresponding calculations to erroneous results. After correcting this erroneous mathematical method, it becomes clear that the problem lies in the initial mathematical algorithm itself, which is used to formulate the theoretical problem of scattering.