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Series solution of the differential equation determining the nth-shell one-electron density of a bare Coulomb problem in quantum physics |
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| Affiliation: | 1. Principal Specialist in Geometric Modelling, DNV GL - Digital Solutions, Veritasveien 1, 1363, Høvik, Norway;2. Department of Mechanical Engineering, University of Western Macedonia, Bakola & Sialvera Str., GR-50132, Kozani, Greece;1. Department of Mathematics, Beijing Technology and Business University, Beijing 100048, China;2. Department of Statistics, University College Cork, Cork, Ireland;3. School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, 100875, Beijing, China;4. Department of Mathematics, Faculty of Science and Technology, University of Macau, Macau (Via Hong Kong) |
| Abstract: | The differential equation determining the nth-shell one-electron density of a bare Coulomb problem is analytically investigated by using the differential function method and extended homogeneous balance idea. New series solution of the differential equation has been obtained in quantum physics for the first time. The explicit series analytical expression for the mathematical characteristic of the bare Coulomb problem in the density-functional theory can further describe the dynamical behaviors of the nth-shell one-electron density. |
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