arXiv subjects
Publications and source records attributed to Runako Williams.
The present article discusses the two point connection problem for Heun's differential equation. We employ a contour integral method to derive connection matrices for a sub-class of the Heun equation containing 3 free parameters. Explicit expressions for the connection coefficients are found.
We review different methods of generating potentials such that the one-dimensional Schr\"{o}dinger equation (ODSE) can be transformed into the hypergeometric equation. We compare our results with previous studies, and complement the subject with new findings. Our main result is to derive new classes of potentials such that the ODSE can be transformed into the Heun equation and its confluent cases. The generalized Heun equation is also considered.