A Green's function approach to the nonrelativistic radial wave equation of hydrogen atom

Abstract

We report an efficient and consistent method for the solution of Schrödinger wave equation using the Green's function technique and its successful application to the nonrelativistic radial wave equation of hydrogen atom. For the radial wave equation, the Green's function is worked out analytically by means of Laplace transform method and the wave function is proposed under the boundary conditions. Computationally the product of potential term, the proposed wave function and the Green's function are integrated iteratively to get the nonrelativistic radial wave function. The resultant wave after each iteration is normalized and plotted against the standard nonrelativistic radial wave function. The solution converges to the standard wave with the increasing number of iterations. Results are verified for the first 15 states of hydrogen atom. The method adopted here can be extended to many‐body problem and hope that it can enhance our knowledge about complex systems.

A scheme of numerical solution for three‐dimensional isoelectronic series of hydrogen atom using one‐dimensional basis functions

“…In atomic structure calculations, the Schrödinger wave equations are usually solved with the use of various approximations, except for the hydrogen atom which carries only one electron . The difficulty of solving the equation exactly for other atoms containing multiple electrons arises from the electronic correlation.…”