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Factorization Ladders and Eigenfunctions

Published online by Cambridge University Press:  20 November 2018

G. F. D. Duff
G. F. D. Duff*
Affiliation:
University of Toronto
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The eigenfunctions of a boundary value problem are characterized by two quite distinct properties. They are solutions of ordinary differential equations, and they satisfy prescribed boundary conditions. It is a definite advantage to combine these two requirements into a single problem expressed by a unified formula. The use of integral equations is an example in point. The subject of this paper, namely the Schrödinger-Infeld Factorization Method, which is applicable to certain restricted. Sturm-Liouville problems, is based upon another combination of the two properties. The Factorization Method prescribes a manufacturing process.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 1 , Issue 4 , 01 August 1949 , pp. 379 - 396
Copyright
Copyright © Canadian Mathematical Society 1949

References

[1] Truesdell, C. A., A Unified Theory of Special Functions (Princeton, 1948).Google Scholar
[2] Infeld, L., Phys. Rev., vol. 59 (1941), 737 contains a discussion of these ladders.Google Scholar
[3] Infeld, L. and Stevenson, A. F. C.. In preparation.Google Scholar
[4] Szegö, G., “Orthogonal Polynomials,” Amer. Math. Soc. Colloquium Publications, vol. 23.Google Scholar
[5] Hull, T. E., thesis, forthcoming.Google Scholar
[6] Schrödinger, E., Proc. Roy. Irish Acad., vol. A46 (1940) 9-16, where the Kepler problem in the spherical space was first considered.Google Scholar
[7] Infeld, L. and Schild, A. E., Phys. Rev., vol. 67 (1945) 121 Google Scholar