A Gaussian wavepacket approach for including correlation in the time-dependent Hartree wavefunction for short times

A hybrid Gaussian wavepacket time-dependent Hartree approach to quantum dynamics is presented. The time-dependent Hartree method yields an efficient methodology for solving the multi-dimensional time-dependent Schrِdinger equation, but has the deficiency of enforcing a factorized form of the wavepacket for all time. We present a strategy for including the correlations in the time-dependent Hartree wavefunction by including a time-dependent correction to the Hartree wavefunction. This correction has the form of a time-dependent Gaussian wavepacket. We test the hybrid Gaussian wavepacket-time-dependent Hartree approach and find that it is able to predict correlations in the wavefunctions for at least a single vibrational period.