Abstract:  There are many approachs to construct quasi-exact solvable problems, such as supersymmetric method, Darboux method, Lie algebra method, etc., but the quasi-exact solvable problems constructed by these methods are often polynomial wave functions. Starting from a class of double well with parametric variation, we study the properties related to the parameters, and find a method to construct QES potential. The QES potential constructed by this method has Lie algebraic structure, but the form of the wave function is non-polynomial.

Key words:  Schrodinger equation, Huen function, quasi-exact and solvable