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. 
@article{TMF_2018_197_2_a4,
     author = {V. N. Likhachev and G. A. Vinogradov},
     title = {Integral characteristics of wave packets in the~problem of the~evolution of a~wave function on a~one-dimensional lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {257--268},
     publisher = {mathdoc},
     volume = {197},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_2_a4/}
}
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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/