  In this paper, we reformulate the semi-classical Schr\"odinger equation in
the presence of electromagnetic field by the Gaussian wave packets transform.
With this approach, the highly oscillatory Schr\"odinger equation is
equivalently transformed into another Schr\"odinger type wave equation, the $w$
equation, which is essentially not oscillatory and thus requires much less
computational effort. We propose two numerical methods to solve the $w$
equation, where the Hamiltonian is either divided into the kinetic, the
potential and the convection part, or into the kinetic and the
potential-convection part. The convection, or the potential-convection part is
treated by a semi-Lagrangian method, while the kinetic part is solved by the
Fourier spectral method. The numerical methods are proved to be unconditionally
stable, spectrally accurate in space and second order accurate in time, and in
principle they can be extended to higher order schemes in time. Various one
dimensional and multidimensional numerical tests are provided to justify the
properties of the proposed methods.
