We investigate electron systems in single- (SPQW) and coupled double parabolic quantum wells (DPQW). The samples are grown with molecular beam epitaxy using the analogue growth technique. The DPQW sample is designed so that in the regions occupied by electrons the bare potential of the wells remains parabolic to a great extent even if the electron occupation is altered. In the experiments the electron density is controlled by a gate. Far-infrared transmission and capacitance experiments demonstrate the nearly parabolic potential of the SPQW. In the DPQW the coupling of the wells is reflected in the occurrence of additional resonances with strong gate voltage dependence of the resonance positions.