As a rule, the Schrödinger equations for systems with more than one interacting particle are impossible to solve exactly. However, quantum chemists have discovered a class of model systems -- consisting of n electrons moving freely on the surface of a sphere -- whose Schrödinger equations can be solved easily. The resulting wavefunctions give us valuable insight into the ways that electrons behave in complicated molecules.
The quantum many-body problem is also present in nuclear physics, where one tries to describe atomic nuclei as a system of strongly interacting nucleons. Nucleons share similarities with electrons in the sense that they are both fermions, and thus obey the Pauli exclusion principle. They also exhibit differences: unlike electrons, nucleons can be found in two species (neutrons and protons), and their interaction is attractive and short range.
The project is to extend the model of electrons on a sphere, developed in the context of quantum chemistry, to systems of nucleons interacting via the strong interaction which is essentially attractive and which acts at short distances. As in molecules, this could give us valuable information on the quantum properties of atomic nuclei.
Note: This is a joint project between Theoretical Physics (Prof Cedric Simenel) and Quantum Chemistry (Prof Peter Gill)