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A G reen's function approach to the nonrelativistic radial wave equation of hydrogen atom
Author(s) -
Ur Rahman Faiz,
Zhang RuiQin
Publication year - 2017
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.25360
Subject(s) - radial function , wave function , green's function for the three variable laplace equation , hydrogen atom , function (biology) , green's function , laplace's equation , laplace transform , schrödinger equation , wave equation , mathematical analysis , physics , boundary value problem , quantum mechanics , mathematics , evolutionary biology , group (periodic table) , biology
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.