Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Acosta-Humánez, M.F., Acosta-Humánez, P.B., Tuirán, E.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209858
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory / M.F. Acosta-Humánez, P.B. Acosta-Humánez, E. Tuirán // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 51 назв. — англ.

In this paper, we start with proving that the Schrödinger equation (SE) with the classical 12−6 Lennard-Jones (L-J) potential is nonintegrable in the sense of the differential Galois theory (DGT), for any value of energy; i.e., there are no solutions in closed form for such a differential equation....