We present a review of rigorous mathematical results about non– adiabatic transitions in molecular systems that are associated with avoided crossings of electron energy level surfaces. We then present a novel numerical technique for studying these transitions that is based on expansions in semiclassical wavepackets.

We investigate the transition of a quantum wave-packet through a onedimensional avoided crossing of molecular energy levels when the energy levels at the crossing point are tilted. Using superadiabatic representations, and an approximation of the dynamics near the crossing region, we obtain an explicit formula for the transition wavefunction. Our results agree extremely well with high precision...

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0 F 3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the ano...

We study the existence and location of resonances a 2×2 semiclassical system coupled Schrödinger operators, in case where two electronic levels cross at some point, one them is bonding, while other anti-bonding. Considering energy just above that crossing, we find asymptotics both real parts imaginary close to such energies. This continuation our previous works considered around crossing.