Particle Trajectories For Compton Scattering in One Space Dimension

Using a relativistic extension of Bohmian Me-chanics known as Multi-Time Wave Function formula-tion, we examine a two-body, one-dimensional sys-tem consisting of one photon and one electron that interact only upon contact. We investigate the effects that various parameters in this theory including mo-mentum of the incoming photon and mass of the electron have on the dynamics of the two interact-ing bodies with the goal of understanding conser-vation of momentum and energy in the system. We show that the core principles of Compton scattering remain when we use this alternative formulation of quantum mechanics. Although a complete relativ-istic theory of Bohmian mechanics has yet to be de-veloped, our work aims to make the ideas in this the-ory more accessible to a wider audience.