Tracing Quantum Trajectories using the PIQTr Model

The path integral technique is an alternative formulation of quantum mechanics that is based on a Lagrangian approach. In its exact form, it is completely equivalent to the Hamiltonian-based Schr\"{o}dinger equation approach. We have used the path integral formalism to develop our Path Integral Quantum Trajectory (PIQTr) model for use in the study of charged particle dynamics. We will present results for several one-dimensional systems, and demonstrate the method's ability to analyze individual trajectories and their influence on the total probability amplitude. We will also show how the range of included trajectories can affect the time evolution of the wave function, resulting in interference fringes reminiscent of those observed with single slit Fresnel diffraction.