Dispersion relations in the non-relativistic theory

Abstract

Stationary co lision th ory, de 1. -ith ele e ts of the scattering ' nd transi ion atrices for p rticular v lu s of n,rgy. U cful gener 1 r suIts Can be obt- in d fro the assu ed sy etry nd unitarity of the .Matrix. General r su Its of a diff rent "ind nr~ obt in· if the S nd T trices . re con id r d to be functions of co pIe .. ', in tend of real hy ic n l para et rs li~e en rgy, cattering ngle, ongul r • In other 'or th conv ntional Sand T atric 5 re nalyticnl1Y continu d into the c pI x pl.n • Tb region ... o£ r gulat-ity, location of singulariti s, th ir atur and charact re tiCS, i£ no , are determine , th n, c uchy th 'Y b us_u to expr in a co pact for the n lytic prop rtie of the continu s- otrix. Thi athe atic~l expr sion is then call d a Di p raion Relation.