  A comparative analysis of three different time-independent approaches to
studying open quantum structures in uniform electric field $\mathscr{E}$ was
performed using the example of one-dimensional attractive or repulsive
$\delta$-potential and surface that supports the Robin boundary condition. The
three considered methods exploit different properties of the scattering matrix
$S(\mathscr{E};E)$ as a function of energy $E$: its poles, real values, and
zeros of the second derivative of its phase. The essential feature of the
method of zeroing the resolvent, which produces complex energies, is the
unlimited growth of the wave function at infinity, which is, however,
eliminated by the time-dependent interpretation. The real energies at which the
unitary scattering matrix becomes real correspond to the largest possible
distortion, $S=+1$, or its absence at $S=-1$ which in either case leads to the
formation of quasibound states. Depending on their response to increasing
electric intensity, two types of field-induced positive energy quasibound
levels are identified: electron- and hole-like states. Their evolution and
interaction in enlarging field lead ultimately to the coalescence of pairs of
opposite states, with concomitant divergence of the associated dipole moments
in what is construed as an electric breakdown of the structure. The
characteristic features of the coalescence fields and energies are calculated
and the behavior of the levels in their vicinity is analyzed. Similarities
between the different approaches and their peculiarities are highlighted; in
particular, for zero-field bound state in limit of vanishing $\mathscr{E}$, all
three methods produce same results, with their outcomes deviating from each
other according to growing electric intensity.
