The Equality of Schrödinger’s Theory and Heisenberg’s S-matrix Theory

Abstract

It is well known that the Schrödinger’s equation can be solved in few cases of physical importance [1] . Nevertheless, S-matrix theory can be used in general to describe physically important variables such as differential cross section, total cross section, etc….[2]. Since there’s no any justification of theoretical work to the best of our knowledge to verify that the Schrödinger’s theory and Heisenberg’s S-matrix theory are equivalent in case of important interacting potentials for which the Schrödinger’s equation can be solved analytically, we have used Heisenberg’s S-matrix theory and Schrödinger’s wave mechanics to justify that the two theories give exactly the same eigenvalues in cases which we have examined. To obtain them, we were able to find the discrete energy eigenvalues in closed form in Heisenberg’s theory without graphical methods.