Eur. Phys. J. Plus (2022) 137: 835
https://doi.org/10.1140/epjp/s13360-022-03029-3

Regular Article

Sextic anharmonic oscillators and Heun differential equations

¹ Instituto de Matemática, Universidad Autónoma de Santo Domingo, Santo Domingo, Dominican Republic
² Department of Mathematics, University of Central Florida, 32816, Orlando, Florida, USA
³ School of Mathematical and Computational Sciences, University of Prince Edward Island, 550 University Avenue, C1A 4P3, Charlottetown, PEI, Canada

^c nsaad@upei.ca

Received: 17 May 2022
Accepted: 1 July 2022
Published online: 20 July 2022

Abstract

With certain constraints on the parameters ${\mu }_4$ and ${\mu }_2$, it is known that the Schrödinger equation with the sextic anharmonic oscillator potential $V(r)=r^6+{\mu }_4{r}^4+{\mu }_2{r}^2$ is quasi-exactly solvable. Here, we solve the Schrödinger equation for arbitrary values of the potential parameters in the d-dimensional case. The method discussed offers a practical solution to the biconfluent Heun equation’s eigenvalue problem. A technique based on the asymptotic iteration method is used to evaluate the coefficients of the series solutions for arbitrary ${\mu }_4$ and ${\mu }_2$.