THE PERIODIC-TABLE IN FLATLAND

The D-dimensional Coulomb system serves as a starting point for genera ting generalized atomic shells. These shells are ordered according to a generalized Madelung rule in D dimensions. This rule together with a n Aufbau Prinzip is applied to produce a D-dimensional periodic table. A model is developed to rationalize the ordering of the shells predic ted by the generalized Madelung rule. This model is based on the intro duction of a Hamiltonian, invariant under the q-deformed algebra U-q(s o(D)), that breaks down the SO(D + 1) dynamical symmetry of the hydrog en atom in D dimensions. The D = 2 case (Flatland) is investigated in some detail. It is shown that the neutral atoms and the (moderately) p ositive ions correspond to the values q = 0.8 and q = 1, respectively, of the deformation parameter q. (C) 1996 John Wiley & Sons, Inc.