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The periodic table in flatland
Author(s) -
Negadi T.,
Kibler M.
Publication year - 1996
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/(sici)1097-461x(1996)57:1<53::aid-qua6>3.0.co;2-y
Subject(s) - periodic table , hamiltonian (control theory) , coulomb , hydrogen atom , invariant (physics) , physics , mathematical physics , quantum mechanics , theoretical physics , mathematics , mathematical optimization , group (periodic table) , electron
The D ‐dimensional Coulomb system serves as a starting point for generating generalized atomic shells. These shells are ordered according to a generalized Madelung rule in D dimensions. This rule together with an Aufbau Prinzip is applied to produce a D ‐dimensional periodic table. A model is developed to rationalize the ordering of the shells predicted by the generalized Madelung rule. This model is based on the introduction of a Hamiltonian, invariant under the q ‐deformed algebra U q (so( D )), that breaks down the SO( D + 1) dynamical symmetry of the hydrogen atom in D dimensions. The D = 2 case (Flatland) is investigated in some detail. It is shown that the neutral atoms and the (moderately) positive ions correspond to the values q = 0.8 and q = 1, respectively, of the deformation parameter q . © John Wiley & Sons, Inc.