We revisit multi-slit diffraction with a scaling of space and time to exploit an equivalence of wave packets describing quantum free and harmonic oscillator (HO) motion. We introduce a co-moving frame of space and time coordinates to define an effective, time-independent, HO potential that confines and directs initially displaced wave packets along the classical phase space of the oscillator. $N$-slit diffraction in the lab frame from the slits to a distant detector and the familiar spreading of the propagating wave front is then described as the propagation of HO wave packets over just a quarter cycle of the oscillator and confined to the HO potential well. We show that diffraction features are preserved in the co-moving frame and well characterized in both the near and far fields by the classical trajectories of the HO phase space.