Radial Wave Functions in Variational Modified WKB Approach: Application to the Modified Pöschl-Teller Potential and Morse Potential

Abstract

Approximate radial wave functions for an arbitrary potential are constructed by means of explicit summation of the leading partial WKB series with the help of a varied power-law substitution. The optimal value of a variational parameter is found from the minimality condition for integral discrepancy. The proposed approach is applied to the modified Pöschl-Teller potential and Morse potential which can be used for adequate simulation of spherical quantum dots.