%0 Journal Article
%T Analytic matrix elements of the Schr dinger equation
%A M. I. Bhatti
%J Advanced Studies in Theoretical Physics
%D 2013
%I
%X A previously defined analytic technique of constructing matrix elementsfrom the Bernstein-polynomials (B-poly) has been applied toSchrˇ§odinger equation. This method after solving generalized eigenvalueproblem yields very accurate eigenenergies and eigenvectors. The numericaleigenvectors and eigenvalues obtained from this process agreewell with exact results of the hydrogen-like systems. Furthermore, accuracyof the numerical spectrum of hydrogen equation depends on thenumber of B-polys being used to construct the analytical matrix elements.Validity of eigenvalues and quality of the constructed wavefunctionsis verified by evaluating the Thomas-Reiche-Kuhn (TRK) sumrules. Excellent numerical agreement is seen with exact results of hydrogenatom.
%K Hydrogen-like systems
%K Schr dinger equation
%K Quantum System
%K Bernstein-Polynomials
%K Energy Spectrum
%U http://www.m-hikari.com/astp/astp2013/astp1-4-2013/bhattiASTP1-4-2013.pdf