We analyze the nonstationary vibrational states prepared by ultrashort laser pulses interacting with a two electronic level molecular system. Fully quantum mechanical expressions are derived for all the moments of the coordinate and momentum operators for the vibrational density matrices associated with the ground and excited electronic states. The analysis presented here provides key information concerning the temperature and carrier frequency dependence of the moments, and relates the moments to equilibrium absorption and dispersion line shapes in a manner analogous to the "transform methods" previously used to describe resonance Raman scattering. Particular attention is focused on the first two moments, for which simple analytical expressions are obtained that are computationally easy to implement. The behavior of the first two moments with respect to various parameters such as the pulse carrier (center) frequency, pulse width, mode frequency, electron-nuclear coupling strength, and temperature is investigated in detail. Using rigorous analytical formulas, we also discuss the laser pulse induced squeezing of the nuclear distributions as well as the pulse induced vibrational heating/cooling in the ground and excited states. The moment analysis of the pump induced state presented here offers a convenient starting point for the analysis of signals measured in pump-probe spectroscopy. The moment analysis can also be used, in general, to better understand the material response following ultrashort laser pulse excitation.