Is fourier analysis unavoidable?

[shevechron]

From the beginning of quantum mechanics the main tool for mathematical analysis was Fourier anaysis. (Heisenberg intoduced his famous matrices using Fourier analysis). Fourier analysis has a non-local character-that the basis functions extend infinitely in space and time. What would be the physical implications if we used a local analytical method, e.g wavelets. This has been proposed by J.R. Croca:

http://redshift.vif.com/JournalFiles/Pre2001/V06NO3PDF/V06N3cro.pdf

In this paper the author claims, uncertainty relations are due to use of Fourier analysis and using wavelets we can go beyond the uncertainity limit.

I'm waiting for ideas!

 

[Valerie Park]

The use of wavelets as an alternative to Fourier analysis in quantum mechanics has the potential to open up a range of new possibilities. It is possible that wavelets could provide a more accurate description of certain physical phenomena, due to their ability to represent localized information. Wavelets could also be used to study the behavior of quantum systems in regimes where the effects of non-locality are important, such as in the context of entanglement. Additionally, wavelets may give insight into the nature of quantum uncertainty, as the author of the paper suggests.