An Eigenfunction Expansion For The Schrodinger Equation With Energy-dependent Potential

In this paper, we consider the eigenfunction expansion problem of the Schrodinger equation with energy-dependent potential under the Sturm-Liouville boundary value by resorting to the complex function method. First, we discuss the rank of an eigenvalue and the order of the zero to corresponding entire function, then calculate the solution of nonhomogeneous problem by constituting Green function, and obtain the expansion theorem in (?)[0,1] through the method of contour integration and the asymptotic ap-proximation method.