Main research findings
Quantum mechanics governs the behavior of atoms and molecules and underpins the properties of nearly everything we can observe. Its laws can be expressed through a single equation —the Schrödinger equation —which researchers use to simulate chemical reactions and predict chemical properties. Such simulations are essential tools in the development of new materials and pharmaceuticals.
This PhD thesis focuses on two cornerstone simulation methods in quantum chemistry: coupled-cluster theory and density functional theory, and establishes a rigorous mathematical foundation for them using advanced tools from functional analysis and C*-algebra.
The thesis consists of three scientific articles addressing key theoretical challenges. The first develops a framework for estimating errors in coupled-cluster calculations, increasing confidence in computational results. The second analyzes the time-dependent bivariational principle, a fundamental concept underlying time-dependent quantum simulations. The third proposes a new, reduced mathematical formulation of density functional theory, offering a more elegant approach to studying electron density. Together, these contributions strengthen the mathematical underpinnings of simulation methods that chemists rely on daily to discover new medicines and technologies.
Members of the evaluation committee
- Professor Eric Cances
Ecole des Ponts ParisTech, France - Doctor Mohammad Hassan
Technische Universität München, Germany - Professor Unni Olsbye (administrative member)
Department of Chemistry, University of Oslo, Norway
Chair/leader of the defense
Professor Ola Nilsen. Department of Chemistry, University of Oslo, Norway.
Funded by
RCN CoE program, Hylleraas Centre. RCN Large Interdisciplinary Researcher Project (Fellesløft IV) QOMBINE: “Mathematics for quantum computation and many-body theory” , https://www.mn.uio.no/math/english/research/projects/qombine/