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

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

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 Schrödinger equation with an inverted quasiexactly solvable potential as well as to the angular equation for an electron in the …