Wave Function Spectroscopy in Quantum Wells with Tunable Electron Density

We present a new approach to investigate quantum-mechanical probability density distributions of electrons in a screened wide potential well, based on low-temperature magnetotransport measurements. Differences of subband energy levels shifted by an inserted controlled potential perturbation are measured and used to extract the difference of the squared amplitude of the respective wave functions at the location of the potential spike. The position of the wave functions and the carrier density can be tuned independently via front- and back-gate voltages. We find excellent agreement between the measured data and self-consistently calculated wave functions.