  The results of systematic experimental studies of quantum oscillations of
resistivity, Hall coefficient and capacitance in GaAs and In$_x$Ga$_{1-x}$As
quantum wells (QWs) with a simple electron spectrum and HgTe QWs with a
complicated non-parabolic spectrum and strong spin-orbit interaction are
reported. A striking result is the ratio of the amplitudes of the resistance
and Hall coefficient oscillations. In GaAs QW with a simple spectrum
characterized by negligibly small Zeeman and spin-orbit splitting, the ratio of
amplitudes is close to that predicted theoretically. In HgTe QWs, this ratio is
very different and behaves differently in QWs with normal and inverted electron
spectra. In HgTe WQs with a normal spectrum, it tends to a theoretical value
with an increase of the filling factor ($N$), while for HgTe QWs with an
inverted spectrum, it differs significantly from the theoretical one for all
available $N$. It is assumed that such a difference in the ratio of amplitudes
in GaAs and HgTe QWs is due not to the peculiarities of the energy spectrum of
HgTe, but to the peculiarities of electron scattering due to spin-orbit
interaction with the potential of the scatterers. This assumption is justified
by analysis of experimental results obtained for a heterostructure with a
In$_{0.2}$Ga$_{0.8}$As QW, which spectrum is very close to the GaAs QW
spectrum, but characterizes by much stronger spin-orbit splitting value. It has
been found that the positions of the resistance and capacitance oscillations,
the difference between the phases of the resistance and Hall coefficient
oscillations and its $N$ dependence are close to those observed in GaAs QW. At
the same time the ratio of the amplitude of the resistance oscillations to the
Hall coefficient oscillations and its $N$ dependence differs very strongly and
they are close to that observed in HgTe quantum wells.
