  Some isolated neutron stars show harmonically spaced absorption features in
their thermal soft X-ray spectra. The interpretation of the features as a
cyclotron line and its harmonics has been suggested, but the usual explanation
of the harmonics as caused by relativistic effects fails because the
relativistic corrections are extremely small in this case. We suggest that the
features correspond to the peaks in the energy dependence of the free-free
opacity in a quantizing magnetic field, known as quantum oscillations. The
peaks arise when the transitions to new Landau levels become allowed with
increasing the photon energy; they are strongly enhanced by the square-root
singularities in the phase-space density of quantum states in the case when the
free (non-quantized) motion is effectively one-dimensional. To explore
observable properties of these quantum oscillations, we calculate models of
hydrogen neutron star atmospheres with B \sim 10^{10} - 10^{11} G (i.e.,
electron cyclotron energy E_{c,e} = 0.1 - 1 keV) and T_{eff} = 1 - 3 MK. Such
conditions are thought to be typical for the so-called central compact objects
in supernova remnants, such as 1E 1207.4-5209 in PKS 1209-51/52. We show that
observable features at the electron cyclotron harmonics form at moderately
large values of the quantization parameter, b_{eff} = E_{c,e}/kT_{eff} = 0.5 -
20. The equivalent widths of the features can reach 100 - 200 eV; they grow
with increasing b_{eff} and are lower for higher harmonics.
