Abstract
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 {\it 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 an 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 with some details. 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
.