Quantum point contacts are fundamental building blocks for mesoscopic
transport experiments and play an important role in recent interference- and
fractional quantum Hall experiments. However, it is not clear how
electron-electron interactions and the random disorder potential influence the
confinement potential and give rise to phenomena like the mysterious 0.7
anomaly. Novel growth techniques of GaAs/AlGaAs heterostructures for
high-mobility two-dimensional electron gases enable us to investigate quantum
point contacts with a strongly suppressed disorder potential. These clean
quantum point contacts indeed show transport features that are obscured by
disorder in standard samples. From this transport data, we are able to extract
the parameters of the confinement potential which describe its shape in
longitudinal and transverse direction. Knowing the shape (and hence the slope)
of the confinement potential might be crucial to predict which
interaction-induced states can form in quantum point contacts
