Classical spin in a potential field

We consider an ensemble of restricted discrete random walks in 2+1 dimensions. The restriction on the walks is such as to given particles an intrinsic angular momentum. The walks are embedded in a field which affects the mean free path of the walks. We show that the dynamics of the walks is such that second-order effects are described by a discrete form of Schrödinger's equation for particles in a potential field. This provides a classical context of the equation which is independent of its quantum context.