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A limit of the confluent Heun equation and the Schroedinger equation for an inverted potential and for an electric dipole

Journal Article · · Journal of Mathematical Physics
DOI:https://doi.org/10.1063/1.3268591· OSTI ID:21294527
;  [1]
  1. Centro Brasileiro de Pesquisas Fisicas (CBPF), Rua Dr. Xavier Sigaud, 150, Rio de Janeiro, Rio de Janeiro CEP 22290-180 (Brazil)
We re-examine 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 Schroedinger equation with an inverted quasiexactly 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.
OSTI ID:
21294527
Journal Information:
Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 50; ISSN JMAPAQ; ISSN 0022-2488
Country of Publication:
United States
Language:
English

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