The classical Hamiltonian  Mean Field model (HMFM) is a one-dimensional toy model, that was initially proposed to study the effects of long-range interactions in statistical mechanics(such as gravity). The classical Hamiltonian is sufficiently simple that certain features in its many body dynamics are calculable in some limit. This has allowed for direct comparison with statistical mechanical predictions. In contrast only static analysis exists for the quantum HMFM, and its dynamics remain an open question. In this talk I will introduce the full many body problem, and then discuss a mean-field approximation involving a Bose-Einstein condensate. In this treatment we can study the dynamics of an order-parameter by employing a self-consistent, mean field, Schrödinger equation. Computational problems will be highlighted and emphasized as they are encountered.