Phys. Rev. Lett. 85, 5022–5025 (2000)Time Evolution of Quantum FractalsReceived 18 May 2000; published in the issue dated 11 December 2000 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 Pt(x) = |Ψ(x,t)|2 is shown not to change during the time evolution. We prove a universal relation Dt = 1+Dx/2 linking the dimensions of space cross sections Dx and time cross sections Dt of the fractal quantum carpets. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.85.5022
DOI:
10.1103/PhysRevLett.85.5022
PACS:
03.65.Ge, 05.45.Df
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