Scanning tunneling spectroscopy (STS) is used to investigate the local density of states of the paradigmatic electron system located in the quasi‐parabolic conduction band of InAs. The n‐InAs(110) surface is used to investigate the system in all dimensionalities (0D‐3D) at low temperatureT= 6 K and in magnetic fields up toB= 6 T. Depending on the dimensionality and theB‐field, we identify different types of electron phases. In particular, we find Bloch‐like wave functions scattered at dopants in 3D atB= 0 T, more complex wave functions reminiscent of weak localization in 2D atB= 0 T and drift states in 2D and 3D atB= 6 T. In 1D, we find surprisingly that the results are explained by a single‐particle calculation, although the energy scales are dominated by electron‐electron interaction. © 2003 American Institute of Physics