Applications of singular analysis to quantum many-particle models in chemistry

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Many interesting problems in condensed matter physics and large parts of chemistry can be described by quantum many-particle systems interacting via singular Coulomb potentials. The subject of this proposl is to study the asymptotic behaviour of such systems, in particular in electronic structure theory, near coalescence ponts of particles using methods from singular analysis. It is intended to provide explicit asymptotic constructions for parametrices of quantum echanical Hamiltonians which encode the asymptotic behaviour of the corresponding solutions of Schrödinger’s equation This can be achieved in the framework of a general pseudo-differential calculus on manifolds with geometric singularities. Here, the Coulomb potentials introduce a natural hierachry of singularities which can be described within the calculus by embedded conical, edge and higher-order corner singularities. A new important feature of the project is to consider not only the Schrödlinger’s equation but also some simplifie many-particle models in the framework of coupled cluster theory. This provides a new perspective concerning the asymptotic behaviour of these models and reveals possible shortcomings which in turn might lead to improved models for electronic structure calculations.