2009/02/18 by Léa Jaccoud El-Jaick, Lea Jaccoud El-Jaick, El-Jaick, Lea Jaccoud +2
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.0902.3202
The proof of convergence, section II.C, was modified
openalex publication_date 2009/02/18 · arxiv created 2009/06/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We reexamine and extend a group of solutions in series of Bessel functions for a limiting case of the confluent Heun equation and, then, apply such solutions to the one-dimensional Schrödinger equation with an inverted quasi-exactly solvable potential as well as to the angular equation for an electron in the field of a point electric dipole. For the first problem we find finite- and infinite-series solutions which are convergent and bounded for any value of the independent variable. For the angular equation, we also find expansions in series of Jacobi polynomials.