Mathematical and Numerical Methods for Complex Quantum Systems

Numerical methods for nonlinear eigenvalue problems arising in quantum physics and chemistry

Eric Cances

Ecole des Ponts and INRIA

I will review several results on the numerical analysis of nonlinear elliptic eigenvalue problems, obtained in the last three years in collaboration with R. Chakir, L. He and Y. Maday. These results provide new guidelines to design more efficient numerical methods for solving the time-independent Gross-Pitaevskii equation, as well as a variety of widely used electronic structure models (Hartree-Fock, Kohn-Sham, orbital-free DFT).