Change of Variables in Factorization Method for Second-order Functional Equations

Abstract

The factorization is a well-known method of solving difference and differential equations. We discuss the change of variables in the approach based on the notion of generalized derivative operator. It is shown that the method is equivariant with respect to the change of variables. Example related to the case of Rosen-Morse potential is presented.

Solutions of theq-deformed Schrödinger equation for special potentials

“…where as usual [γ ] := 1−q γ 1−q , see [6,7,9,10]. In the following, according to [6], we will assume that…”