On the Quasi-Exact Solvability of the Confluent Heun Equation
Mathematical Physics
2014-10-07 v2 math.MP
Abstract
It is shown that the Confluent Heun Equation (CHEq) reduces for certain conditions of the parameters to a particular class of Quasi-Exactly Solvable models, associated with the Lie algebra . As a consequence it is possible to find a set of polynomial solutions of this quasi-exactly solvable version of the CHEq. These finite solutions encompass previously known polynomial solutions of the Generalized Spheroidal Equation, Razavy Eq., Whittaker-Hill Eq., etc. The analysis is applied to obtain and describe special eigen-functions of the quantum Hamiltonian of two fixed Coulombian centers in two and three dimensions.
Keywords
Cite
@article{arxiv.1406.2643,
title = {On the Quasi-Exact Solvability of the Confluent Heun Equation},
author = {M. A. Gonzalez Leon and J. Mateos Guilarte and A. Moreno Mosquera and M. de la Torre Mayado},
journal= {arXiv preprint arXiv:1406.2643},
year = {2014}
}
Comments
16 pages, 4 figures. V2: references added, typos corrected