Geodesic
Fractals in quantum theory: analytical and numerical approaches
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 73-79

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Quantum systems whose evolution has a fractal nature are considered for the example of the evolution of a wave packet in quantum mechanics. Quantum states in which the evolution of the expectation values of certain operators are described by fractal curves are constructed. The fractal dimensions of these curves are calculated. The presence of an exact analytical result makes it possible to compare the different methods of calculating the fractal dimensions. 
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P. K. Silaev; E. N. Tyurin; O. A. Khrustalev. Fractals in quantum theory: analytical and numerical approaches. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 73-79. http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a6/