Generalized optical theorem

Abstract We present the generalized optical theorem and its applications with special emphasis on roles of bound states. First, we prove which gives a necessary sufficient condition for function $\langle {\bf {\it k}^{\prime}} | T k}} \rangle$ two variables $\ k}}^{\prime }$ ${\bf k}}$ to be physically acceptable as half-on-shell T-matrix, i.e., have an underlying Hermitian potential V. Second, using theorem, construct scattering theory starting from T-matrix } \rangle$, in turn introduces very useful classification scheme potentials. In end, application our theory, most general solution inverse problem numerical examples.