The Factorization Method

L. Infeld; T. E. Hull

doi:10.1103/RevModPhys.23.21

The Factorization Method

L. Infeld and T. E. Hull

Rev. Mod. Phys. 23, 21 – Published 1 January 1951

Abstract

The factorization method is an operational procedure which enables us to answer, in a direct manner, questions about eigenvalue problems which are of importance to physicists. The underlying idea is to consider a pair of first-order differential-difference equations which are equivalent to a given second-order differential equation with boundary conditions. For a large class of such differential equations the method enables us to find immediately the eigenvalues and a manufacturing process for the normalized eigenfunctions. These results are obtained merely by consulting a table of the six possible factorization types.

The manufacturing process is also used for the calculation of transition probabilities.

The method is generalized so that it will handle perturbation problems.

DOI:https://doi.org/10.1103/RevModPhys.23.21

Authors & Affiliations

L. Infeld^*

University of Toronto, Toronto, Ontario, Canada

T. E. Hull^†

University of British Columbia, Vancouver, British Columbia, Canada

^*Now at the Physics Institute, Warsaw, Poland.
^†Part of this report was submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the University of Toronto, 1949.