Estimates of the type L₁-L_∞ for the Schrödinger Equation on the Line and on Half-Line with a regular potential V(x), express the dispersive nature of the Schrödinger Equation and are the essential elements in the study of the problems of initial values, the asymptotic times for large solutions and Scattering Theory for the Schrödinger equation and non-linear in general; for other equations of Non-linear Evolution. In general, the estimates L_p-L_p' express the dispersive nature of this equation. And its study plays an important role in problems of non-linear initial values; likewise, in the study of problems nonlinear initial values; see [1] [2] [3]. On the other hand, following a series of problems proposed by V. Marchenko [4], that we will name Marchenko’s formulation, and relate it to a generalized version of Theorem 1 given in [1], the main theorem (Theorem 1) of this article provides a transformation operator W that transforms the Reduced Radial Schrödinger Equation (RRSE) (whose main characteristic is the addition a singular term of quadratic order to a regular potential V(x)) in the Schrödinger Equation on Half-Line (RSEHL) under W. That is to say; W eliminates the singular %K The Schrö %K dinger Equation on the Half-Line %K Reduced Radial Equation of Schrö %K dinger %K Conditions Sufficient to Establish the Uniqueness of the Potential and Boundary Conditions Are Named the Generalized Theorem 1 %K The Marchenko’s Formulation %K Reduction of Estimates < %K i> %K L< %K /i> %K < %K sub> %K 1< %K /sub> %K -< %K i> %K L< %K /i> %K < %K sub> %K & %K #8734 %K < %K /sub> %K for the Reduced Radial Equation of Schrô %K dinger to Equation on Half-Line %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=92728