Energy dependent coordinate bending for quantum dynamics of screened Coulomb potential systems

This work aims to examine the power of an energy dependent coordinate mapping to facilitate the solution to Schrödinger equations for screened Coulomb potential systems.The model system is taken as two particle system in only interparticle distance dependent potential which is also spherically symmetric. Since time independent Schrödinger equation of such system can be reduced to relative motion separated out of angular coordinates, the wave function becomes dependent on relative radial variable only and the motion can be investigated more easily. The energy parameter is taken as -v²/2 since only bound states are considered. First an unknown coordinate bending function is defined in terms of the coordinate and energy arguments. After appropriate assumptions the resulting spectral problem is solved and the potential function is obtained in terms of coordinate bending function which we called "Characteristic Potential for the Coordinate Bending". Then appropriate efficient coordinate bending structures can be sought to somehow match the Characteristic potential with the true given potential and system energy can also be identified through this procedure.