  It is pointed out that there exists an interesting strong and weak duality in
the Landau-Zener-Stueckelberg potential curve crossing. A reliable perturbation
theory can thus be formulated in the both limits of weak and strong
interactions. It is shown that main characteristics of the potential crossing
phenomena such as the Landau-Zener formula including its numerical coefficient
are well-described by simple (time-independent) perturbation theory without
referring to Stokes phenomena. A kink-like topological object appears in the
``magnetic'' picture, which is responsible for the absence of the coupling
constant in the prefactor of the Landau-Zener formula. It is also shown that
quantum coherence in a double well potential is generally suppressed by the
effect of potential curve crossing, which is analogous to the effect of Ohmic
dissipation on quantum coherence.
