Physics – Mathematical Physics
Scientific paper
2010-09-02
J. Phys. A:Math. Theor. 43, 415206 (2010)
Physics
Mathematical Physics
13 pages, no figures
Scientific paper
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.
Ciftci Hakan
Dogu Ebubekir
Hall Richard L.
Saad Nasser
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