Doctor of Philosophy / Department of Physics / Brett D. Esry / The nuclear rotational period of the simplest molecule H[subscript]2[superscript]+ is about 550 fs, which is more than 35 times longer than its vibrational period of 15 fs. The rotational time scale is also much longer than widely available ultra short laser pulses which have 10 fs or less duration. The large difference in rotational period and ultra short laser pulse duration raises questions about the importance of nuclear rotation in theoretical studies of H[subscript]2[superscript]+ dissociation by these pulses. In most studies, reduced-dimensionality calculations are performed by freezing the molecular axis in one direction, referred to as the aligned model. We have systematically compared the aligned model with our full-dimensionality results for total dissociation probability and field-free dynamics of the dissociating fragments. The agreement between the two is only qualitative even for ultra short 10 fs pulses. Post-pulse dynamics of the bound wave function show rotational revivals. Significant alignment of H[subscript]2[superscript]+ occurs at these revivals. Our theoretical formulation to solve the time-dependent Schrodinger equation is an important step forward to make quantitative comparison between theory and experiment. We accurately calculate observables such as kinetic energy, angular, and momentum distributions. Reduced-dimensionality calculations cannot predict momentum distributions. Our theoretical approach presents the first momentum distribution of H[subscript]2[superscript]+ dissociation by few cycle laser pulses. These observables can be directly compared to the experiment. After taking into account averaging steps over the experimental conditions, we find remarkable agreement between the theory and experiment. Thus, our theoretical formulation can make predictions. In H[subscript]2[superscript]+ dissociation by pulses less than 10 fs, an asymmetry in the momentum distribution occurs by the interference of different pathways contributing to the same energy. The asymmetry, however, becomes negligible after averaging over experimental conditions. In a proposed pump-probe scheme, we predict an order of magnitude enhancement in the asymmetry and are optimistic that it can be observed.