Elementary Theory of Scattering

Abstract

In some of the earlier chapters we had considered solutions of the Schrödinger equation which correspond to bound state problems where the wave function vanished at large distances from the origin; the corresponding energy levels were found to form a discrete set. In this chapter we will consider solutions of the Schrödinger equation where the energy eigenvalues would be continuously distributed; for such a case the wave function would not vanish at large distances from the origin. Such solutions correspond to the scattering of a particle by a force field where the energy is specified in advance and the behaviour of the wave function is found in terms of energy. We should mention here that in Chapter 8 we did consider the scattering by a one-dimensional force field, the corresponding three-dimensional case will be considered here.

Our actual situation in research work in atomic physics is usually this: we wish to understand a certain phenomenon, we wish to recognise how this phenomenon follows from the general laws of nature. Therefore, that part in the phenomenon is the natural ‘object’ in the theoretical treatment and should be separated in this respect from the tools used to study the phenomenon. This again emphasises a subjective element in the description of atomic events, since the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning.

Werner Heisenberg in Physics and Philosophy, Penguin, London (1989).