10.5281/zenodo.1089211
https://zenodo.org/records/1089211
oai:zenodo.org:1089211
Said Laachir
Said Laachir
Aziz Laaribi
Aziz Laaribi
Exact Solutions of the Helmholtz equation via the Nikiforov-Uvarov Method
Zenodo
2013
Helmholtz equation
Nikiforov-Uvarov method
exact solutions
eigenfunctions.
2013-11-03
eng
10.5281/zenodo.1089210
https://zenodo.org/communities/waset
9996665
Creative Commons Attribution 4.0 International
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 Nikiforov-Uvarov (NU) method. It is found that the solution of the angular eigenfunction can be expressed by the associated-Legendre polynomial and radial eigenfunctions are obtained in terms of the Laguerre polynomials. The special case for k=0, which corresponds to the Laplace equation is also presented.