Title: quantum mechanics of fractal potential wells.
Post by: kram1032 on October 30, 2012, 09:25:04 AM
Instead of potentially wondering how quantum-mechanics might apply to fractals, there is actual research on this topic, as found here:
P-adic QM (Wiki) (http://en.wikipedia.org/wiki/P-adic_quantum_mechanics)
Note, there are lots of references to more information on this topic, like, for instance:
Michael Berry's publications (http://www.phy.bris.ac.uk/people/berry_mv/publications.html), for instance the so called "Diffractals (pdf) (http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry080.pdf)" - Waves that have encountered fractals and thus interfered in fractal ways on all scales.
I encourage searching through the references for further info beyond Wikipedia.
P-adic QM (Wiki) (http://en.wikipedia.org/wiki/P-adic_quantum_mechanics)
Note, there are lots of references to more information on this topic, like, for instance:
Michael Berry's publications (http://www.phy.bris.ac.uk/people/berry_mv/publications.html), for instance the so called "Diffractals (pdf) (http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry080.pdf)" - Waves that have encountered fractals and thus interfered in fractal ways on all scales.
I encourage searching through the references for further info beyond Wikipedia.
Title: Re: quantum mechanics of fractal potential wells.
Post by: jehovajah on October 30, 2012, 05:36:59 PM
Righto, Kram. Will give it a shot! ;D
Title: Re: quantum mechanics of fractal potential wells.
Post by: Alef on November 11, 2012, 05:40:42 PM
Could it be created real 3D mandelbrot set on p-adic numbers? Or on adele ring?
Well, it seems not so, even I realy don't understand this concept an I'm not a matematician, but could there be some new fractals based on this?
Well, it seems not so, even I realy don't understand this concept an I'm not a matematician, but could there be some new fractals based on this?
Title: Re: quantum mechanics of fractal potential wells.
Post by: kram1032 on November 11, 2012, 10:44:06 PM
I'm fairly sure (but I'm not an expert either, obviously), that you gotta have a complete limit set description of the set...
Stuff like the usual cantor set, where you end up with a very predictable pattern for the numbers in the set and
-Analogues of it, like the sierpinski carpets, sponges, etc.
I could easily be wrong though.
Stuff like the usual cantor set, where you end up with a very predictable pattern for the numbers in the set and
I could easily be wrong though.