  Quantum tunneling through an almost classical potential barrier can be
strongly enhanced by a nonstationary field so that the penetration through the
barrier becomes not exponentially small. This constitutes an extremely unusual
phenomenon of quantum physics called Euclidean resonance. A certain
nonstationary barrier is proposed with a very low WKB tunneling rate. The
quantum dynamics of this barrier is mapped on resonant tunneling across a
static double barrier with a resonant level inside. The real penetration
through the dynamical barrier is not exponentially small providing an example
of Euclidean resonance. Therefore, the Schoedinger equation allows solutions of
the type of Euclidean resonance. The counterintuitive phenomenon of Euclidean
resonance is a dynamical analogue of static resonant tunneling.
