Radu Budaca†
Abstract: The D-dimensional Schr¨odinger equation for an isotropic sextic potential is brought to a form compatible with the canonical bi-confluent Heun differential equation. The quasi-exactly solvable properties of the model are recovered by considering polynomial solutions for the
bi-confluent Heun equation which constrains the potential parameters in terms of rotation quantum number, space dimension and order of the exact solvability. It is shown that the state independence of the potential can be maintained by using a see-saw adjustment between the rotation quantum number and the exact solvability order. An analysis on the exactly solvable instances of the sextic potential is presented in correlation with the extended set of exactly solvable states.
MSC: 34Axx, 34Bxx, 81Qxx, 81Vxx
keywords: Schr¨odinger equation, Quasi exact solvability, bi-confluent Heun differential equation.
DOI 10.56082/annalsarscimath.2020.1-2.87
† rbudaca@theory.nipne.ro Department of Theoretical Physics, ”Horia Hulubei ” National Institute for Physics and Nuclear Engineering, Reactorului 30, RO-077125, POB-MG6, Bucharest Magurele, Romania; Academy of Romanian Scientists, 54 Splaiul Independeței, RO-050094, Bucharest, Romania
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 12 no 1-2, 2020
