The overall objective is to develop analytical tools---mainly from the theory of partial differential equations---suitable for the description of large quantum mechanical systems with singular (Coulomb) interaction. The overall objective can be broken up into six parts which relate to the following six work packages:
1. Desingularization of Singular Partial Differential Operators 2. Description of Ground State Properties of Complex Atoms and Molec. 3. Relation Between the Thermodynamic and Semi-Classical Limit 4. Pointwise Behavior of Eigenfunctions
5. Non-Asymptotic Eigenvalue Estimates
6. Stability of Relativistic Quantum Systems
The problems related to these topics are motivated by concrete questions from physics and concretely defined but aim at a development of ---microlocal---analysis for singular pseudo-differential operators. The network will provide training for six postdoctoral scientists in the area of analysis / partial differential operators/ mathematical physics. The problems being clearly defined and motivated by concrete applications, the proposed work is in particular suitable for young scientist who have, however, a solid background in analysis. Since most of the research work packages require the cooperation of two or more teams the young researchers will be able to draw from the scientific capacities of more than one team.
CF24 4YH Cardiff
91405 425 Orsay
8000 Århus C