Wave Propagation in Crystal Lattices and N Coupled Harmonic Oscillators

Indianapolis, IN

In this article we studied wave propagation in crystal lattices as the motion of a chain of coupled harmonic oscillators. We analytically solved for fixed ends of the chain and for one end driven by harmonic force with the other end fixed. In both scenarios, we considered the ideal frictionless case as well as the case of frictional force proportional to velocity. General features of the motion were captured by analyzing the motion of two and six masses. We investigated questions of resonance and energy exchange, and concluded with a comparison with quantum lattice excitations (phonons).