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The Factorization Method

L. Infeld* and T. E. Hull†

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

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

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.

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

    © 1951 American Physical Society

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