Physics – Quantum Physics
Scientific paper
2001-09-28
Chaos, Solitons & Fractals 14, 823-830 (2002)
Physics
Quantum Physics
Scientific paper
10.1016/S0960-0779(02)00027-9
Physical fractals invariably have upper and lower limits for their fractal structure. Berry has shown that a particle sharply confined to a box has a wave function that is fractal both in time and space, with no lower limit. In this article, two idealizations of this picture are softened and a corresponding lower bound for fractality obtained. For a box created by repeated measurements (\`a la the quantum Zeno effect), the lower bound is $\Delta x\sim \Delta t (\hbar/{mL})$ with $\Dt$ the interval between measurements and $L$ is the size of the box. For a relativistic particle, the lower bound is the Compton wavelength, $\hbar/mc$. The key step in deriving both results is to write the propagator as a sum over classical paths.
No associations
LandOfFree
Limits of fractality: Zeno boxes and relativistic particles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Limits of fractality: Zeno boxes and relativistic particles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Limits of fractality: Zeno boxes and relativistic particles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-155379