Quantum Painlev´e II solution with approximated analytic solution in form of nearly Yukawa potential

In this article it has been shown that one dimensional non-stationary Schrodinger equation with a specific choice of potential reduces to the quantum Painleve II equation and the solution of its riccati form appears as a dominant term of that potential. Further, we show that Painleve II Riccati solution is an equivalent representation of centrifugal expression of radial Schrodinger potential. This expression is used to derive the approximated to the Yukawa potential of radial Schrodinger equation which can be solved by applying the Nikiforov-Uvarov method. Finally, we express the approximated form of Yukawa potential explicitly in terms of quantum Painleve II solution.