Morlet wavelets in quantum mechanics - Quantum PhysicsReport as inadecuate

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Abstract: Wavelets offer significant advantages for the analysis of problems in quantummechanics. Because wavelets are localized in both time and frequency they avoidcertain subtle but potentially fatal conceptual errors that can result from theuse of plane wave or delta function decomposition. Morlet wavelets areparticularly well-suited for this work: as Gaussians, they have a simpleanalytic form and they work well with Feynman path integrals. To take fulladvantage of Morlet wavelets we need an explicit form for the inverse Morlettransform and a manifestly covariant form for the four-dimensional Morletwavelet. We supply both here.

Author: John Ashmead


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