The periodic table in flatland

✍ Scribed by T. Negadi; M. Kibler

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 681 KB
• Volume: 57
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1996)57:1<53::aid-qua6>3.0.co;2-y

✦ Synopsis

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 Aufoau Prinzip is applied to produce a Ddimensional 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,(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 4.