We present an original method for the accurate quantum treatment of the planar three body Coulomb problem under electromagnetic driving. Our ab initio approach combines Floquet theory, complex dilation, and the representation of the Hamiltonian in suitably chosen coordinates without adjustable parameters. The resulting complex-symmetric, sparse banded generalized eigenvalue problem of rather high dimension is solved using advanced techniques of parallel programming. In the present thesis, this theoretical/numerical machinery is employed to provide a complete description of the bound and of the doubly excited spectrum of the field-free 2D helium atom. In particular, we report on frozen planet quantum states in planar helium. For the driven atom, we focus on the near resonantly driven frozen planet configuration, and give evidence for the existence of nondispersive two-electron wave packets which propagate along the associated periodic orbit. This represents a highly nontrivial qualitative confirmation of earlier calculations on a 1D model atom, though with important enhancements of the decay rate of these atomic eigenstates in the field, due to the transverse decay channel. The latter is already found to enhance the decay rates of the unperturbed frozen planet as compared to the 1D model, in surprisingly good quantitative agreement with 3D results.