2014/06/10 by M. A. González León, J. Mateos Guilarte, Leon, M. A. Gonzalez +5
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum, superfluid, helium dynamics
paper · pdf · doi:10.48550/arxiv.1406.2643
openalex publication_date 2014/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.