Université Libre de Bruxelles, Belgique.

What mathematicians know about the solutions of Schrodinger Coulomb Hamiltonian. Should chemists care?

Abstract :

The Coulomb Hamiltonian has been an object of study by mathematicians

since the 1930s but the first big advance was made by Kato in 1951 when he

showed that it actually had solutions and he was

able to determine the differentiablity and analyticity properties of the

solutions. From then on, much was discovered about solutions for neutral

atoms and positive atomic ions and a little about negative atomic ions.

From a mathematical point of view the Coulomb Hamiltonian with clamped

nuclei is much like the atomic problem and so the mathematical properties

of the results of the usual electronic structure calculations are

well-understood. However almost nothing is known about the properties of

its solutions for molecular systems when the nuclei are not treated as

clamped. So from a mathematical point of view it cannot, as yet, be said

that the full Coulomb Hamiltonian explains the existence of molecules.

The origin of this rather uncomfortable position will be the subject of

the talk.