Fractality of Certain Quantum States |
| D.K. Wójcika, b, K. Życzkowskic, d
aNencki Institute of Experimental Biology of Polish Academy of Sciences, Pasteura 3, 02-093 Warsaw, Poland bInstitute of Applied Psychology, Jagiellonian University, Łojasiewicza 4, 30-348 Kraków, Poland cInstitute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków, Poland dCenter for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 26-680 Warszawa, Poland |
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| Fractal structures appearing in solutions of certain quantum problems are investigated. We prove the previously announced results concerning the existence and properties of fractal states for the Schrödinger equation in the infinite one-dimensional well. In particular, we show that for this problem, there exist solutions in the form of fractal quantum carpets: the probability density P(x,t) forms a fractal surface with dimension Dxy, while its cross-sections Pt(x) and Px(t) typically form fractal graphs with dimensions Dx and Dt respectively, where Dxy=2+Dx/2 and Dt=1+Dx/2 (almost everywhere). |
DOI:10.12693/APhysPolA.143.146 topics: quantum carpets, quantum fractals, fractal dimension, fractal curves |