  The problem of resonant excitation of a harmonic oscillator the energy levels
of which are slightly shifted under the action of a random potential is solved.
It is shown that, in this case, there exists a threshold magnitude of the
exciting resonance field, below which the excitation is localized on lower
levels, and above which the oscillator is indefinitely excited so that it is
necessary to take into account dissipative processes. A method similar to that
developed for the oscillator is applied to examine the localization of
electrons in a wire with cross-section varying along its length. It is shown,
in particular, that there is no localization if this variation is superlinear.
