  In this report we present preliminary results about the tunneling problem for
a magnetic Schr\"odinger operator. As a motivation we consider the 3-D
time-dependent Schr\"odinger operator $H(t)=-h^2\Delta+V+E(t)\cdot x$ where $V$
is a radial potential and $E(t)$ a circularly polarized field with uniform
frequency $\omega$. The quantum monodromy operator (QMO) that takes the system
through a complete period $T=2\pi/\omega$, turns out to be unitarily equivalent
to $e^{iTP_A(x,hD_x)/h}$, where $P_A(x,hD_x))$ identifies with a magnetic
Schr\"odinger operator. When $V$ is sufficiently confining, $P_A(x,hD_x))$
presents a double magnetic well. Then we construct its semi-classical ground
state and examine the splitting between its two first eigenvalues.
