This paper explores the quantum fluid dynamical (QFD) representation of the time-dependent Schrodinger equation for the motion of a wave packet in a high dimensional space. A novel alternating direction technique is utilized to single our each of the many dimensions in the QFD equations. This technique is used to solve the continuity equation for the density and the equation for the convection of the flux for the quantum particle. The ability of the present scheme to efficiently and accurately describe the dynamics of a quantum particle is demonstrated in four dimensions where analytical results are known. We also apply the technique to the photodissociation of NOCl and NO2 where the systems are reduced to two coordinates by freezing the angular variable at its equilibrium value.