  A magnetotransport and quantum capacitance of the two-dimensional electron
gas in HgTe/Cd$_x$Hg$_{1-x}$Te quantum wells of a width ($20.2-46.0$)~nm are
experimentally investigated. It is shown that the first energy subband of
spatial quantization is split due to the spin-orbit interaction and the split
branches are single-spin, therewith the splitting strength increases with the
increase of the quantum well width. The electron effective masses in the
branches are close to each other within the actual density range.
Magneto-intersubband oscillations (MISO) observed in the structures under study
exhibit the growing amplitude with the increasing electron density that
contradicts to the expected decrease of wave function overlap for the
rectangular quantum well. To interpret the data obtained, we have used a
self-consistent approach to calculate the electron energy spectrum and the wave
function within framework of the \emph{kP}-model. It has been in particular
shown that the MISO amplitude increase results from the increasing overlap of
the wave functions due to their shift from the gate electrode with the gate
voltage increase known as phenomenon of the negative electron polarizability.
The results obtained from the transport experiments are supported by quantum
capacitance measurements.
