Detailseite
Projekt
Regularity, complexity, and approximability of electronic wavefunctions
Antragsteller
Professor Dr. Harry Yserentant
Fachliche Zuordnung
Mathematik
Förderung
Förderung von 2008 bis 2016
Projektkennung
Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 79767058
The project considers the electronic Schrödinger equation of quantum chemistry that describes themotion of N electrons under Coulomb interaction forces in a field of clamped nuclei. Solutions ofthis equation depend on 3N variables, three spatial dimensions for each electron. Approximatingthe solutions is thus inordinately challenging. It is conventionally believed that the accuracy cannotbe systematically improved without the effort truly exploding for larger numbers of electronsand that a reduction to simplified models, such as those of the Hartree-Fock method or densityfunctional theory, is the only tenable approach for the approximation of the solutions. Resultsof the applicant indicate that this conventional wisdom need not be ironclad: The regularity ofthe solutions, which increases with the number of electrons, the decay behavior of their mixedderivatives, and the antisymmetry enforced by the Pauli principle contribute properties that allowthese functions to be approximated with an order of complexity which comes arbitrarily close tothat of a system of two electrons or even only one electron. Goal of the project is to extend andrefine these results and to identify structural properties of the wavefunctions that could ideallyenable breaking the curse of dimensionality and to develop the present approximation methodsfurther to true discretizations of the Schrödinger equation.
DFG-Verfahren
Schwerpunktprogramme
