Dynamics of quantum observables and Born's rule in Bohmian Quantum Mechanics

In the present paper we study both ordered and chaotic Bohmian trajectories in the Born distribution of 2d quantum systems. We find theoretically and numerically the average values of the energy, momentum, angular momentum and position of 2d quantum systems. In particular, we consider realizations of the Born distribution of a system with a single nodal point and of two different cases with many nodal points, one with almost equal number of ordered and chaotic trajectories and one consisting of almost exclusively chaotic trajectories. The numerical average values agree with the theoretical values if the Born P=|Ψ|² rule is initially satisfied, but do not agree when P₀≠|Ψ₀|². We study the role of ordered and chaotic trajectories in providing these average values.