School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
2013
Abstract
A previously defined analytic technique of constructing matrix elements from the Bernstein-polynomials (B-poly) has been applied to Schr¨odinger equation. This method after solving generalized eigenvalue problem yields very accurate eigenenergies and eigenvectors. The numerical eigenvectors and eigenvalues obtained from this process agree well with exact results of the hydrogen-like systems. Furthermore, accuracy of the numerical spectrum of hydrogen equation depends on the number of B-polys being used to construct the analytical matrix elements. Validity of eigenvalues and quality of the constructed wavefunctions is verified by evaluating the Thomas-Reiche-Kuhn (TRK) sum rules. Excellent numerical agreement is seen with exact results of hydrogen atom.
Recommended Citation
Bhatti, Muhammad I. "Analytic Matrix Elements of the Schrödinger Equation." Adv. Stud. Theor. Phys 7.11 (2013). http://dx.doi.org/10.12988/astp.2013.13002
Publication Title
Adv. Stud. Theor. Phys
DOI
10.12988/astp.2013.13002
Comments
Copyright © 2013 M. I. Bhatti. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.