Alternating direction implicit technique and quantum evolution within the hydrodynamical formulation of Schrِdingerʹs equation

An alternative method of quantum dynamics is presented. The method is based on the hydrodynamical formulation of the time-dependent Schrِdinger equation originally given by David Bohm in his quest for establishing a hidden variable alternative to the quantum mechanics. A new alternating direction implicit technique has been employed to decouple many-dimensional hydrodynamical equations into a set of one-dimensional equations which have been solved numerically by adopting a recently developed flux corrected transport algorithm. We apply the method to describe the dynamics of a quantum particle in three spatial dimensions where analytical solutions are known.