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arXiv · 1406.2643

On the Quasi-Exact Solvability of the Confluent Heun Equation

M. A. Gonzalez Leon·J. Mateos Guilarte·A. Moreno Mosquera·M. de la Torre Mayado
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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 $sl (2,{\mathbb R})$. 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.

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M. A. Gonzalez Leon, J. Mateos Guilarte, A. Moreno Mosquera, M. de la Torre Mayado. 2014-06-10. On the Quasi-Exact Solvability of the Confluent Heun Equation. https://arxiv.org/abs/1406.2643

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