This thesis advances our understanding of quantum phases and their interplay with particle trajectories in closed and open Bohmian systems, employing the innovative QuantumVelocity Search Algorithm to reconstruct wave functions and perform bulk phase statistics. Analysis of closed systems reveals significant insights into velocity distributions and positional velocity constraints. In closed systems, the analysis uncovered that modulating the initial phase on the expansion coefficients for the energy eigenstates, as well as the number of terms in the expansion, significantly influences positional velocity characteristics. The number of terms restricts the maximum velocity that can be achieved. For example, 4 terms produce 1 Å/fs at the center of the box compared to 300 Å/fs with 18 terms. Many different sets of initial phase values can lead to the same velocity. Open systems are modeled by dynamically changing the phase factors as a stochastic process to model the influence of the environment. Examination of open systems highlights their disruptive effect on the quantum behavior for a closed system, with the phase diffusion coefficient being linked to rates of thermal energy transfer into and out of the system. The relationship between energy rates and phase coefficients creates a maximal energy rate because angle deviations repeat every 2?. This research underscores the alternative perspectives between determinism in chaotic systems compared to a probabilistic interpretation in quantum mechanics, setting a foundation for future exploration of open quantum systems within the Bohmian framework.