An approach to one-dimensional

elliptic quasi-exactly solvable models

M A FASIHI¹, M A JAFARIZADEH^2,3,4 and M REZAEI^2,*

¹Department of Physics, Azarbijan University of Tarbiat Moallem, Tabriz 53714-161, Iran

²Department of Theoretical Physics and Astrophysics, Tabriz University, Tabriz 51664, Iran

³Institute for Studies in Theoretical Physics and Mathematics, Tehran 19395-1795, Iran ⁴Research Institute for Fundamental Sciences, Tabriz 51664, Iran

^*Corresponding author

E-mail: ma-fasihi@azaruniv.edu; Jafarizadeh@tabrizu.ac.ir;

karamaty@tabrizu.ac.ir

Abstract. One-dimensional Jacobian elliptic quasi-exactly

solvable second-order differential equations are obtained by

introducing the generalized third master functions. It is shown

that the solutions of these differential equations are generating

functions for a new set of polynomials in terms of energy with

factorization property. The roots of these polynomials are the

same as the eigenvalues of the differential equations. Some

one-dimensional elliptic quasi-exactly quantum solvable models are

obtained from these differential equations.

Keywords. Quasi-exactly solvable potential; master function.

PACS No. 03.65.Ud