Conservation Theorem and the Method of Moments in Quantum Scattering

The unitary condition, or the constraint imposed by the conservation of probability, is examined for certain approximate solutions to physical scattering problems. The unitary condition is shown to be preserved for an approximate nonrelativistic S matrix derived by a rather generalized moments method. The unitary condition, or conservation theorem, is shown to be satisfied independent of the accuracy of the approximate solution under certain specifically defined conditions.