Property C and the I-function of the one dimensional inverse scattering problems

In this work we investigate the property C and the I-function of the one dimensional inverse scattering problem. First we constitude scattering data for -u^''+q(x)u=k^2 u Sturm-Liouville differential equation under some initial conditions. After that we define and investigate the property C which gives the completeness feature for the solutions of the above initial value problem for Sturm-Liouville differential equation. Then we introduce the I-function which is known empedance function and the I-function is useful for inversion procedures and to find the potential function q(x). Finally we glance at Marchenko and Gelfand-Levitan inversion procedure and their applications.