Said Laachir and Aziz Laaribi Exact Solutions of the Helmholtz equation via the NikiforovUvarov Method
170 - 173
2013
7
1
International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering http://waset.org/publications/9996665
http://waset.org/publications/73
World Academy of Science, Engineering and Technology
The Helmholtz equation often arises in the study of physical problems involving partial differential equation. Many researchers have proposed numerous methods to find the analytic or approximate solutions for the proposed problems. In this work, the exact analytical solutions of the Helmholtz equation in spherical polar coordinates are presented using the NikiforovUvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associatedLegendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k0, which corresponds to the Laplace equation is also presented.
International Science Index 73, 2013