The Factorization Method

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.