A Contribution to the Quantum Mechanical Theory of Radioactivity and the Dissociation by Rotation of Diatomic Molecules

Publisher Website
Google Scholar
Abstract
In the recent theory of radioactive decay, and also, as is shown, in the theory of dissociation of a diatomic molecule by the acquisition of rotational energy, there occurs a potential energy curve which has the following shape, as we go, say, from left to right. At the left the potential energy is very high, it then comes down to a minimum, increases to a maximum, and again falls off to an asymptotic value. The problems connected with such a curve are of two types. First, we may be given a particle in the region near the minimum, in an energy level which lies below the maximum, and wish to find the chance that it appear by a quantum mechanical process in the region on the other side of the maximum. Second, we wish to find how the "discrete states" in the neighborhood of the minimum are "broadened" by the continuum on the other side of the maximum. To solve these problems we first find the stationary eigenfunctions. By means of them the width and shape of the "broadened discrete levels" are found immediately. We then use these eigenfunctions to set up a wave packet, or, rather, we show how nature may set up a wave packet, which enables us to solve the first of the problems mentioned. The result justifies the use of complex eigenvalues for the solution of the problem.

This publication has 20 references indexed in Scilit: