The nanoscale distributions of electron density and electric fields in GaAs semiconductor devices are displayed with NMR experiments. The spectra are sensitive to the changes to the nuclear-spin Hamiltonian that are induced by perturbations delivered in synchrony with a line-narrowing pulse sequence. This POWER (perturbations observed with enhanced resolution) method enhanced resolution up to 103-fold, revealing the distribution of perturbations over nuclear sites. Combining this method with optical NMR, we imaged quantum-confined electron density in an individual AlGaAs/GaAs heterojunction via hyperfine shifts. Fits to the coherent evolution and relaxation of nuclei within a hydrogenic state established one-to-one correspondence of radial position to frequency. Further experiments displayed the distribution of photo-induced electric field within the same states via a quadrupolar Stark effect. These unprecedented high-resolution distributions discriminate between competing models for the luminescence and support an excitonic state, perturbed by the interface, as the dominant source of the magnetically modulated luminescence.