On a particular form of a symmetric P\"oschl-Teller potential
Mathematical Physics
2015-11-10 v2 math.MP
Abstract
We show that solutions of the Schr\"odinger equation with a symmetric P\"oschl-Teller potential of a particular form can be expressed in terms of a closed combination (not series) of trigonometric functions. Using some properties of the eigenfunctions of the Schr\"odinger equation and their inner product we determine a new exact representation of the hypergeometric function with certain values of parameters in terms of a closed combination of trigonometric functions. We also obtain new results in an explicit closed form for integrals with the hypergeometric function and with the specific combination of trigonometric functions.
Keywords
Cite
@article{arxiv.1506.06708,
title = {On a particular form of a symmetric P\"oschl-Teller potential},
author = {Andrei Smirnov and Antonio Jorge Dantas Farias},
journal= {arXiv preprint arXiv:1506.06708},
year = {2015}
}
Comments
7 pages