The Schrödinger equation, the famous basic equation of quantum theory, which Erwin Schrödinger first published in 1926, is almost a hundred years old. With this equation, it was possible for the first time to explain the properties of a hydrogen atom exactly, and since then it has proven itself brilliantly in countless applications.

But the Schrödinger equation has a big problem: when many particles are involved at the same time, it becomes extremely complicated and cannot be solved exactly even with the best supercomputers in the world. And that's a pity – because it's precisely such many-particle phenomena that we often have to deal with in materials physics: How precisely can material properties be calculated? What happens on the surface of a catalyst at the atomic level? How much do certain material surfaces reduce the energy barriers for the production of solar fuels?

Highly endowed grant for Tobias Schäfer

Tobias Schäfer works as a postdoc at the Institute for Theoretical Physics at TU Wien. He is working on novel computational methods that can be used to answer quantum physics questions that would be completely unsolvable if the Schrödinger equation were simply applied naively. He has now received an ESPRIT grant from the FWF for this work, endowed with almost € 300,000.

The FWF's ESPRIT programme aims to support young scientists at an early stage of their research career - the completion of the dissertation may not be more than five years ago. The ESPRIT grant is intended to make it possible to develop an independent research profile and launch an internationally successful career.

Not perfect – but almost

Tobias Schäfer's research project over the next three years will focus on various computational methods for quantum many-body systems.

One of the most important methods in materials research is density functional theory - a physicist who played leading role in the development of density functional theory was Walter Kohn, who was awarded the Nobel Prize in 1998. In practice, the complicated Schrödinger equation is replaced by a mathematically much simpler equation. Certain properties of many-particle systems can be calculated well that way. But if the correlations of many electrons determine the material properties, the density functional theory quickly loses accuracy. Other methods are then needed – a particularly promising candidate for this is the "coupled-cluster method", with which the quantum-physically highly complex interaction of several particles can be recorded very precisely.

"Strictly speaking, you don't get the exact solution, but an approximation that meets the requirements of scientific and also industrial research much better," says Tobias Schäfer. "We are developing a new approach to massively reduce the computational costs and thus significantly expand the scope of the coupled cluster method so that urgent questions can be answered with this method."

The FWF-ESPRIT project "Coupled Cluster Computations for Large Simulation Cells" will officially start on 01.04.2023 and is designed for a total duration of 3 years.