Presseinformation: Zooming in: electron orbitals photographed in 3D

Nr. 103 - 04.08.2026

Physicists at Göttingen University image three-dimensional wavefunctions with table-top, soft-X-ray laser

One of the most famous and intriguing results of quantum mechanics is the finding that fundamental particles, such as electrons, cannot be pinned down to one single location. Instead, a particle is described by its “wavefunction”, which allows researchers to derive probability distributions – a sort of mathematical map that shows the possibilities – of fundamental properties such as its position and momentum. In particular, the electron wavefunctions within a molecule, known as “molecular orbitals”, carry information about how the molecule interacts with its surroundings. For example, it shows how it may absorb light or how a chemical reaction might take place. As a consequence, knowledge of the complete three-dimensional wavefunction is highly desirable, but imaging the wavefunction has proven to be a major experimental challenge. An interdisciplinary research team at the University of Göttingen has now managed to image the three-dimensional wavefunction of a nanometer-sized organic molecule. They overcame the limitations by combining state-of-the-art photoelectron spectroscopy with powerful mathematical algorithms. The results were published in Nature Communications.

“The wavefunction is a fundamental quantity in quantum mechanics, yet it cannot be directly observed or measured,” explains Professor Stefan Mathias at the University of Göttingen. Instead, the team relied on an indirect approach: namely, photoelectron spectroscopy, where the momentum of the emitted electrons is measured to provide access to one half of the wavefunction, without physically altering its state. Sophisticated computer algorithms then deduced the other half, allowing researchers to image the complete molecular orbital and to resolve features that are smaller than the distance between the carbon atoms that make up the molecule. However, applying this principle in 3D previously required time-intensive measurements at large-scale synchrotron facilities, limiting its widespread application and, in particular, its extension towards imaging “dynamical” wavefunctions in a 3D video at the scale of an atom.

Dr Matthijs Jansen, University of Göttingen, and co-leader of the study, highlights the originality of the team’s approach: “We introduce two powerful new concepts. First, by redesigning the computer algorithm from the ground up, reliable 3D images can now be obtained using much less experimental data. Second, the experiment is based upon a powerful, lab-based soft-X-ray light source that provides ultrashort light pulses. It is the combination of these two techniques that has this remarkable impact.” Dr Wiebke Bennecke, first author of the study, adds: “This technique might mean that stroboscopic videography becomes a reality, allowing us to observe not just the shape of wavefunctions, but also to see how it changes with ultrafast, even femtosecond or one quadrillionth of a second, resolution. This will mean we can learn how a molecule adapts to optical, electronic, or chemical changes and find new ways to control these interactions at the level of a few atoms.”

Original publication: Bennecke, W. et al. "Table-top three-dimensional photoemission orbital tomography with a femtosecond extreme ultraviolet light source." Nature Communications (2026). DoI: 10.1038/s41467-026-74308-1

Contact:

Professor Stefan Mathias

University of Göttingen

Ultrafast Dynamics in Quantum Materials Research Group

Faculty of Physics

Friedrich Hund Platz 1, 37077 Göttingen, Germany

Tel: +49 (0)551 39-27601

Email: smathias@uni-goettingen.de

www.mathiaslab.uni-goettingen.de

Dr Matthijs Jansen

University of Göttingen

Ultrafast Dynamics in Quantum Materials Research Group