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

Abstract: We investigate both ordered and chaotic Bohmian trajectories within the Born distribution of Bohmian particles of an anisotropic 2d quantum harmonic oscillator. We compute the average values of energy, momentum, angular momentum, and position using both Standard Quantum Mechanics and Bohmian Mechanics. In particular, we examine realizations of the Born distribution for a wavefunction with a single nodal point and two different wavefunctions with multiple nodal points: one with an almost equal number of ordered and chaotic trajectories, and another composed primarily of chaotic trajectories. Throughout our analysis, we focus on elucidating the contribution of ordered and chaotic Bohmian trajectories in determining these average values.