On the Quasi-Exact Solvability of the Confluent Heun Equation
| Autor: | González León, Miguel Ángel, Mateos Guilarte, Juan María, Moreno Mosquera, Asdrúbal, Torre Mayado, Marina de la |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | GREDOS. Repositorio Institucional de la Universidad de Salamanca instname |
| Popis: | [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. 4 figures. V2: references added, typos corrected |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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