Bouncing photon, relativistic particle and the Maxwell Boltzmann Distribution

The purpose of this short note is to consider properties of a photon bouncing in the x direction in a box moving at a speed v also in the x direction. In particular, we wish to see if such a system yields the energy and momentum of relativistic particle. Next, we wish to see if there may be a physical basis for a wavefunction for the particle. From this conservation of momentum of particles follows using the same arguments used in quantum mechanics. We wish also to see if there may be implications of the quantization of momentum in a one-dimensional well. Finally, we examine whether the Maxwell Boltzmann distribution can possibly be derived from a bouncing photon model.