  The general classical solution of the 3D electromagnetic pp-wave spacetime
has been obtained. The relevant line element contains an arbitrary essential
function providing an infinite number of in-equivalent geometries as solutions.
A classification is presented based on the symmetry group. To the best of our
knowledge, the solution corresponding to only one of the Classes is known. The
dynamics of some of the Classes was also derived from a minisuperspace
Lagrangian which has been constructed. This Lagrangian contains a degree of
freedom (the lapse) which can be considered either as dynamical or
non-dynamical (indicating a singular or a regular Lagrangian correspondingly).
Surprisingly enough, on the space of classical solutions, an equivalence of
these two points of view can be established. The canonical quantization is then
used in order to quantize the system for both the singular and regular
Hamiltonian. A subsequent interpretation of quantum states is based on a
Bohm-like analysis. The semi-classical trajectories deviate from the classical
only for the regular Hamiltonian and in particular for a superposition of
eigenstates (a Gaussian initial state has been used). Thus, the above mentioned
equivalence is broken at the quantum level. It is noteworthy that the
semi-classical trajectories tend to the classical ones in the limit where the
initial wavepacket is widely spread. Hence, even with this simple superposition
state, the classical solutions are acquired as a limit of the semi-classical.
