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On the Possible Forms of Differential Equation which Can be Factorized by the Schrödinger-Infeld Method

Published online by Cambridge University Press:  20 November 2018

A. F. Stevenson  and
W. A. Bassali
A. F. Stevenson
Affiliation:
Farouk I University, Alexandria, Egypt
W. A. Bassali
Affiliation:
Farouk I University, Alexandria, Egypt
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The factorization method, initiated by Schrödinger [4] and modified and developed by Infeld [2], Duff [1], and Infeld and Hull [3], furnishes an elegant method of solving eigenvalue problems associated with certain ordinary differential equations of the second order. Not only the eigenvalues and eigenfunctions can thus be obtained, but also certain matrix elements associated with the eigenfunctions. Even if the method cannot be applied directly to eigenvalue problems, the factorization of an equation may still be of interest, since recurrence formulae may thus be established, e.g. for Bessel functions [3]. The connection of the method with Truesdell's [5] method of the “F -equation” has been discussed by Duff [1].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 385 - 395
Copyright
Copyright © Canadian Mathematical Society 1952

References

1. Duff, G. F. D., Factorization ladders and eigenfunctions, Can. J. Math., vol. 1 (1949), 379–396.Google Scholar
2. Infeld, L., On a new treatment of some eigenvalue problems, Phys. Rev., vol. 59 (1941), 737–747.Google Scholar
3. Infeld, L. and Hull, T. E., The factorization method, Rev. Mod. Phys., vol. 23 (1951), 21–68.Google Scholar
4. Schrödinger, E., Proc. Royal Irish Acad., vol. A46 (1940), 9.Google Scholar
5. Truesdell, C. A., A unified theory of special functions (Princeton, 1948).Google Scholar