QUANTUM PAINLEVÉ II SOLUTION AND APPROXIMATED ANALYTIC SOLUTION OF THE YUKAWA POTENTIAL

Overview & Synopsis

In this paper, it has been shown that one dimensional non- stationary Schrödinger equation with a speci c choice of potential reduces to the quantum Painlevé II equation and the solution of its Riccati form appears as a dominant term of that potential. Further, this article shows that the square of quantum Painlevé II Riccati solution is equivalent to the centrifugal expression of radial schrödinger potential which reduces to the approximated form of Yukawa potential that can be used to solve the radial Schrödinger equation by applying the Nikiforov-Uvarov method.. Finally, I express the approximated form of Yukawa potential explicitly in terms of qunatume Painlevé II solution.