Analytical Solution for 3D Stationary Schr\"{o}dinger Equation: application to scattering

We have derived and studied the generalized Ricatti equation for the WKB approximation in three dimensions. A new approximated solution of Schrodinger equation is obtained. We show that this solution is more accurate than that of the WKB method. Writing Schrodinger differential equation in an integral form which is suitable for scattering theory, we discuss some applications of the obtained results, in particular, to the scattering problem.