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

作者：El Jaick Lea Jaccoud^*; Figueiredo Bartolomeu D B

来源：Journal of Mathematical Physics, 2009, 50(12): 123511.

DOI：10.1063/1.3268591

• Bessel functions
• polynomials
• Schrodinger equation

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 Schroumldinger 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.

• 出版日期2009-12