The text is organized as follows. We begin with the summary of the article "Determination of a linear differential equation on half-line and its spectral distribution function from the others related". The first part, a simplified description is made of the antecedents. The second part, it is shown a brief and simplified state of art of the inverse problems corresponding to the inverse scattering is offered both in the one-dimensional case and the multidimensional case. The third part: On the determination of the linear differential of the second order on half-line and its spectral distribution function. Where we offer a simplified version of the background used and the fundamental of existence and uniqueness of the second problem in relation to the first Sturm-Liouville problem. The fourth part: two fundamental examples related in the previous sense are exhibited. The importance of The Estimates L₁-L∞ for the Equation of Schr ndinger on the Half-Line is mentioned. In Open Problems, the possibility of obtaining a generalization of the previous estimates is mentioned. Finally, a simplified list of the references used for this text is offered.