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Título
On the Quasi-Exact Solvability of the Confluent Heun Equation
Autor(es)
Materia
Mathematical physics
Mathematical Physics
Fecha de publicación
2014
Resumen
[EN] 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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Colecciones
- MATHPHYS. Artículos [94]