A clear
understanding of the mechanisms that control the electron
dynamics in a strong laser field is still a challenge that requires
interpretation by advanced theory. Development of accurate theoretical
and computational methods, able to provide a precise treatment of
the fundamental processes generated in the strong field regime, is
therefore crucial. A central aspect is the choice of the basis for
the wave function expansion. Accuracy in describing multiphoton processes
is strictly related to the intrinsic properties of the basis, such
as numerical convergence, computational cost, and representation of
the continuum. By explicitly solving the 1D and 3D time-dependent
Schrödinger equation for H2+ in the presence
of an intense electric field, we explore the numerical performance
of using a real-space grid, a B-spline basis, and a Gaussian basis
(improved by optimal Gaussian functions for the continuum). We analyze
the performance of the three bases for high-harmonic generation and
above-threshold ionization for H2+. In particular,
for high-harmonic generation, the capability of the basis to reproduce
the two-center interference and the hyper-Raman phenomena is investigated.