The hydrogen exchange reaction has a conical intersection and is therefore a prototype for studying geometric phase effects in reaction dynamics. We compute wave packets in hyperspherical coordinates for the reaction H + H 2 ( v 0=0, j 0=0) → H 2 + H, over the collision energy range E coll=0.75−2.02 eV, using the plane wave packet method. Geometric phase effects are not included. The wave packets visualise the quantum dynamics around the conical intersection and relate it to the centre-of-mass scattering angle. The wave packet fails to encircle the conical intersection, making slightly less than half a revolution. This provides a physical picture for why geometric phase effects in this reaction are expected to be reduced.