  A field dependent $su(2)$ gauge transformation connects between the adiabatic
and diabatic pictures in the (Landau-Zener-Stueckelberg) potential curve
crossing problem. It is pointed out that weak and strong potential curve
crossing interactions are interchanged under this transformation, and thus
realizing a naive strong and weak duality. A reliable perturbation theory
should thus be formulated in the both limits of weak and strong interactions.
In fact, 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. We also show 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.
