Quantum Painlevé II solution and Approximated analytic solution of the Yukawa Potential

Abstract

We show that one dimensional non-stationary Schrödi-nger equation with a specific 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, we show that Painlevé II Riccati solution is an equivalent representation of centrifugal expression of radial Schrödinger potential. This expression is used to derive the approximated form of the Yukawa potential of radial Schrödinger equation which can be solved by applying the Nikiforov-Uvarov method. Finally, we express the approximated form of Yukawa potential explicitly in terms of qunatume Painlevé II solution.

arXiv commentThis article encloses some mistakes and results are need to be corrected