Integral Characteristics of Wave Packets in the Problem of the Evolution of A Wave Function on A One-Dimensional Lattice
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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.
Keywordsquantum dynamics tight-binding approximation moments of distribution function
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- 8.V. A. Benderskii and E. I. Kats, “Propagation of excitation in long 1D chains: Transition from regular quantum dynamics to stochastic dynamics,” JETP, 116, 1–14.Google Scholar