The initial conditions and outcomes of this type of process are encoded in an S-matrix.
One scheme for solving these types of problems which is useful in classical situations is the Lax-Phillips formalism. If the Wightman conditions, which include relativistic invariance of states and the existence and uniqueness of a vacuum are satisfied, then the Haag-Ruelle theory may be used to solve quantum mechanical problems of this type. One result that gives a way of extracting a quantity relevant to processes of this type is the optical theorem. The probability amplitude associated with this process can be given as the Fourier transform of the potential involved in this process in accordance with the Born approximation. The initial conditions and outcomes of this type of process are encoded in an S-matrix. For ten points, identify this type of problem in physics, solving which typically involves finding the cross section.
One scheme for solving these types of problems which is useful in classical situations is the Lax-Phillips formalism.
{scattering}