Simulating quantum particle trajectories within an infinite square well

The Copenhagen interpretation has long dominated quantum mechanics, while Bohmian mechanics (BM) offers a deterministic, statistically equivalent alternative. BM treats particles and the wavefunction as distinct entities, allowing particles to follow precise trajectories with simultaneous position and velocity. This study examines BM under the equilibrium hypothesis, where velocity is derived from the probability current density. BM is applied to the infinite square well problem for one particle in one and two dimensions, as well as two entangled particles (bosons and fermions) in one dimension. The wavefunctions are initialized in thermodynamic equilibrium at various temperatures. Using MATLAB, simulations visualize particle trajectories, with the quantum potential generating non-classical forces confining particles. Although energy fluctuates over time due to the non-conservative quantum potential, the average energies agree with predictions from standard calculations. Periodic trajectories are observed for the one-dimensional single-particle case, while ergodic behavior is found in the other systems. The initial phases significantly impact the trajectories, which have ramifications to open quantum systems