Geodesic
Integral characteristics of wave packets in the problem of the evolution of a wave function on a one-dimensional lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 257-268
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We consider the quantum dynamics of charge transfer on a lattice in the tight-binding approximation and analytically calculate the integral characteristics of the wave packet propagating along the lattice. We focus on calculating the mean and root-mean-square displacements. We also obtain expressions for higher-order moments as series for squares of Bessel functions, which might be independently interesting.
Keywords: quantum dynamics, tight-binding approximation, moments of distribution function. 
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V. N. Likhachev; G. A. Vinogradov. Integral characteristics of wave packets in the problem of the evolution of a wave function on a one-dimensional lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 2, pp. 257-268. http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a4/

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