  Wavelets offer significant advantages for the analysis of problems in quantum
mechanics. Because wavelets are localized in both time and frequency they avoid
certain subtle but potentially fatal conceptual errors that can result from the
use of plane wave or delta function decomposition. Morlet wavelets are
particularly well-suited for this work: as Gaussians, they have a simple
analytic form and they work well with Feynman path integrals. To take full
advantage of Morlet wavelets we need an explicit form for the inverse Morlet
transform and a manifestly covariant form for the four-dimensional Morlet
wavelet. We supply both here.
