Related Experiment Video
Updated: Oct 10, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Time evolution of quantum fractals
Wojcik1, Bialynicki-Birula, Zyczkowski
1Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/46, 02-668 Warszawa, Poland and College of Science (Szkola Nauk Scislych), Al. Lotnikow 32/46, 02-668 Warszawa, Poland.
Abstract:
We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential, and free particle. The box-counting dimension of the probability density P(t)(x) = |Psi(x,t)|(2) is shown not to change during the time evolution. We prove a universal relation D(t) = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections D(t) of the fractal quantum carpets.
Related Concept Videos
The de Broglie Wavelength
Interference and Diffraction
The Quantum-Mechanical Model of an Atom
The Bohr Model
Emission Spectra
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.