Summary
A method to obtain solutions of a restricted class of Sturm-Liouville’s 2nd-order ordinary differential equations in an easy and elegant way is presented in this work. The method does not cover all kinds of possible Sturm-Liouville’s equations of the 2nd-order but only a restricted class of equations which, nevertheless, are important in the mathematical-physics field. Just to mention a few: Legendre, Hermite, Laguerre, Chebyshev, Jacobi, Gegenbauer equations belong to this class. The method gives two infinite sets of eigenfunctions almost by inspection. In this frame, Dirac’s annihilation and creation operators can be derived as a particular case. The problem of shifted equations is solved and that of associated one, outlined.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Arfken:Mathematical Methods for Physicists (Academic Press, New York, N.Y., 1970).
A. Messhiah:Mécanique quantique (Dunod, Paris, 1975).
W. G. Kelley andA. C. Peterson:Difference Equation (Academic Press, 1991).
M. L. Boas:Mathematical Methods in the Physical Sciences (J. Wiley and Sons, Inc., New York, N.Y., 1970).
J. T. Cushing:Applied Analytical Mathematics for Physical Scientists (J. Wiley and Sons, Inc., New York, N.Y., 1975).
M. Tenenbaum andH. Pollard:Ordinary Differential Equations (Harper and Row, New York, N.Y., 1963).
J. Lambe andC. J. Tranter:Differential Equations for Engineers and Scientists (Row and Peterson, Evanston, Ill., 1961).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Quartieri, J. Can the application of Heaviside’s method shed new light into a class of Sturm-Liouville’s equations relevant in the mathematical-physics field?. Nuov Cim B 109, 809–820 (1994). https://doi.org/10.1007/BF02722460
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02722460