Construction of accelerating wavepackets

Accelerating wavepackets are obtained by applying the extended Galilean transformation to free-space particle wavepackets, or to time-dependent bound states. The transformed Schrödinger equation contains a potential term, which drives the acceleration. The method reproduces Darwin’s result for an accelerating Gaussian wavepacket in a constant force field, and Schrödinger’s oscillating wavepacket in a harmonic well. We also derive a new accelerating Airy wavepacket in a gravitational field, and give a new derivation of oscillating wavepackets based on the higher harmonic oscillator energy eigenstates. These results illustrate an analytic method of dealing with wavepackets accelerating in force fields.