Mapping Schr\"odinger equation into a Heun-type and identifying the corresponding potential function, energy and wavefunction
Quantum Physics
2020-12-25 v2 Mathematical Physics
math.MP
Abstract
We transform the Schr\"odinger wave equation to a nine-parameter Heun-type differential equation. Using our solutions of the latter in [J. Math. Phys. 59 (2018) 113507], we are able to identify the associated potential function, energy parameter, and write the corresponding wave function. Some of the solutions obtained correspond to new integrable quantum systems.
Cite
@article{arxiv.1906.11162,
title = {Mapping Schr\"odinger equation into a Heun-type and identifying the corresponding potential function, energy and wavefunction},
author = {A. D. Alhaidari},
journal= {arXiv preprint arXiv:1906.11162},
year = {2020}
}
Comments
This revised version corrects a mistake in Eq. (7)