Can fractal mathematics be used in quantum mechanics?

[questionposter]

It seems like the more I look at complex physical systems, the more they have the same patterns I find in fractals.

I can't remember what it's called, but when using sine waves in parametric equations there is sort of a "time" that the function takes in order to return to a previous state and overlap itself, or maybe it's simply called completing a cycle, and this same type of phenomena of repeating occurs in both fractals and wave mechanics, so I was wondering if there was some complex way fractals could be used to describe quantum mechanics and how it evolves to things on the macroscopic level.

Edited April 15, 2012 by questionposter

[Xittenn]

A relative of mine asked me at Easter dinner if there was any such thing as Fractal Engineering. I said to him that in the strictest of sense no, but I'm sure that you can come up with something if the problem fits. I am curious as to what sort of physical system represents itself with a precise nonlinear pattern?

 

Is that you Rick?

[ajb]

I do not know of any way that fractals can be used to replace the standard theory, which is based on operators. That said, fractals do appear in quantum mechanics; you may be interested in the almost Mathieu operator and the Hofstadter's butterfly which arises in the study of the quantum Hall effect.

[Amr Morsi]

I really don't know the word "fractal". What I do know is that it is physical. But, I can serve in a thing: "It is an issue of weighted states. It, as far as I can explain, solves QM in high speeds and high curvatures, in general, in the domain of: High Transitions and Nears to Charges".