Initial phase and free-particle wave packet evolution

Abstract

The evolution of the free-particle wave function in one dimension is the same as scalar Fresnel diffraction from a one-dimensional structure. Quantum mechanics courses often explore the propagation of Gaussian wave packets, but the diffractionlike mathematics is sufficiently tractable to investigate the propagation of other wave packets, both numerically and analytically. More importantly, the diffraction analogy facilitates the development of an intuitive understanding of the role that the initial phase plays in free-particle wave packet evolution. This article considers some of the effects of the initial phase function on the subsequent evolution of free-particle wave packets in the position representation. These considerations reinforce the idea that the classical mechanics limit embodied in the correspondence principle and formalized in the Ehrenfest theorem is necessarily an incomplete representation of quantum behavior.