Physical applications of second-order linear differential equations that admit polynomial solutions
Mathematical Physics
2015-05-19 v1 math.MP
Quantum Physics
Abstract
Conditions are given for the second-order linear differential equation P3 y" + P2 y'- P1 y = 0 to have polynomial solutions, where Pn is a polynomial of degree n. Several application of these results to Schroedinger's equation are discussed. Conditions under which the confluent, biconfluent, and the general Heun equation yield polynomial solutions are explicitly given. Some new classes of exactly solvable differential equation are also discussed. The results of this work are expressed in such way as to allow direct use, without preliminary analysis.
Cite
@article{arxiv.1009.0464,
title = {Physical applications of second-order linear differential equations that admit polynomial solutions},
author = {Hakan Ciftci and Richard L. Hall and Nasser Saad and Ebubekir Dogu},
journal= {arXiv preprint arXiv:1009.0464},
year = {2015}
}
Comments
13 pages, no figures