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

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

2009-02-18

arxiv.org/abs/0902.3202v2

Physics

Mathematical Physics

The proof of convergence, section II.C, was modified

Scientific paper

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 Schr\"odinger 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.

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