“Morlet wavelets in quantum mechanics” updated

The announcement the world has been waiting for can now be made:  the paper “Morlet wavelets in quantum mechanics” has been updated.  The latest version has a much clearer explanation of the point, a number of errors corrected, and some stylistic infelicities eliminated.

This version has been uploaded to the physics archive.


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.

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