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  Quantum mechanics without wavefunctions

   School of Mathematics and Physics

  ,  Applications accepted all year round  Funded PhD Project (Students Worldwide)

About the Project

The world around us is made of atoms and the properties of matter depend on how atoms bond together to form molecules and solids. This happens due to the motion and interactions of electrons and nuclei. To understand this we need quantum mechanics which describes these particles in terms of wavefunctions and the Schrödinger equation.

But solving the Schrödinger equation for a system of interacting electrons and nuclei is a horrendous problem once we get beyond just a few particles. Many decades of physics research has gone into approximate ways of doing that instead.

There is a remarkable trick that enables us to map the problem of electrons and nuclei in a molecule into an effective classical problem that involves interacting classical particles buzzing around and bouncing off each other. This is a much easier problem to solve. Traditionally this trick has been used to study quantum effects in the motion of nuclei. In this project we want to apply it to the electrons instead, and ultimately to the electrons and nuclei together.

This produces a solution to the quantum problem without any of the quantum machinery, i.e. wavefunctions or the Schrödinger equation: a fascinating idea. There still are limitations on the system sizes that can be reached and on the physical conditions studied: this method applies only to equilibrium systems. Nevertheless it remains a very interesting approach to a notoriously hard problem that we wish to apply to the calculation of electron densities and pair correlation functions, polarisability, exchange-correlation energies, and electron-nuclear correlation effects in small molecules and clusters.

Eligibility: UK residents only

For further details please contact and .

Mathematics (25) Physics (29)

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