The mathematics of the periodic table of the elements

DIPC Seminars

Jan Philip Solovej
Dept. of Mathematics, University of Copenhagen
Donostia International Physics Center (hybrid seminar)
Geza Giedke
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The mathematics of the periodic table of the elements

The elements are grouped in the periodic according to their chemical properties. Elements with similar properties form the columns in the periodic table.  The Aufbau principle or Madelung rule gives a phenomenological explanation for the structure of the periodic table. In this talk I will discuss two mathematical results relating to the periodic table. To make general mathematical statements I will allow myself to consider atoms with atomic number much larger than those that exist in nature. The non-relativistic quantum mechanical description of atoms can be studied mathematically for arbitrarily large atomic number. I will ask the following two questions. Does the periodic structure persist for arbitrarily large atoms? Is the Aufbau principle still valid for large atoms? The answer to the second question is no. The Aufbau Principle fails for large atoms. The first question is more difficult and I do not know the answer in general. I will, however, show that in a certain mean field model of atoms there is an exact periodic behavior in the limit of infinitely large atoms.  This is based on work with Bjerg, Fournais, and Hearnshaw.