  We study theoretically the effect of an electric field on the electron states
and far-infrared optical properties in narrow-gap lead salt quantum wells. The
electron states are described by a two-band Hamiltonian. An application of a
strong electric field across the well allows the control of the energy gap
between the two-dimensional (2D) states in a wide range. A sufficiently strong
electric field transforms the narrow-gap quantum well to a nearly gapless 2D
system, whose electron energy spectrum is described by linear dispersion
relations \epsilon_{\sigma} (k) ~\pm (k-k_{\sigma}), where k_{\sigma} are the
field-dependent 2D momenta corresponding to the minimum energy gaps for the
states with spin numbers \sigma. Due to the field-induced shift of the 2D
subband extrema away from k=0 the density of states has inverse-square-root
divergencies at the edges. This property may result in a considerable increase
of the magnitude of the optical absorption and in the efficiency of the
electrooptical effect.
