  The dissociation spectrum of the hydrogen molecular ion by short intense
pulses of infrared light is calculated. The time-dependent Schr\"odinger
equation is discretized and integrated in position and momentum space. For
few-cycle pulses one can resolve vibrational structure that commonly arises in
the experimental preparation of the molecular ion from the neutral molecule. We
calculate the corresponding energy spectrum and analyze the dependence on the
pulse time-delay, pulse length, and intensity of the laser for $\lambda \sim
790$nm. We conclude that the proton spectrum is a both a sensitive probe of the
vibrational dynamics and the laser pulse. Finally we compare our results with
recent measurements of the proton spectrum for 55 fs pulses using a Ti:Sapphire
laser ($\lambda \sim 790 $nm). Integrating over the laser focal volume, for the
intensity $I \sim 3 \times 10^{15}$W cm$^{-2}$, we find our results are in
excellent agreement with these experiments.
