Potentials of the Heun class: the triconfluent case

Autor:	Batic, D., Mills-Howell, D., Nowakowski, M.
Rok vydání:	2014
Předmět:	Mathematical Physics Mathematics - Classical Analysis and ODEs Physics - Chemical Physics
Druh dokumentu:	Working Paper
DOI:	10.1063/1.4921344
Popis:	Since the advent of quantum mechanics different approaches to find analytical solutions of the Schr\"odinger equation have been successfully developed. Here we follow and generalize the approach pioneered by Natanzon and others by which the Schr\"odinger equations can be transformed into another well-known equation for transcendental function (e.g., the hypergeometric equation). This sets a class of potentials for which this transformation is possible. Our generalization consists in finding potentials allowing the transformation of the Schr\"odinger equation into a triconfluent Heun equation. We find the energy eigenvalues of this class of potentials, the eigenfunction and the exact superpartners. Comment: 18 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1412.3847 Zobrazit plný text záznamu View this record from Arxiv