Here I'm thinking of a single free particle obeying the Schroedinger equation. The ensemble refers to multiple experiments with a single particle in which the initial wave function is the same. If I naively imagine that there is such a thing as a wave function that is delta function, in Bohmian mechanics, since the distribution of initial positions in the ensemble is given by the wave function, all particles in the ensemble presumably have the same position. This means that all members of the ensemble have the same trajectory, and there will be no future uncertainty in position. However, the wave function of a free particle does spread out since it is not an eigenstate of the Hamiltonian, and so the Bohmian prediction would not agree with quantum mechanics. Is my error in imagining that (due to wave functions being continuous) there is such a thing is a wave function that is a delta function? If that is the reason for the error, does this mean that Bohmian mechanics wouldn't work if position were discrete?