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Physics Letters A

Exact propagators for time-dependent Coulomb, delta and other potentials

V. V. Dodonov, Vladimir I. Man’ko, Dmitri E. Nikonov

Published Feb 1, 1992• 65 citations
Publisher
DOI
10.1016/0375-9601(92)90054-p

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In this work, we have investigated the Gaussian and Airy wave packets colliding on the Dirac delta potentials. We have used the time-dependent space-fractional Schrodinger equation and solved it by using the slit step finite difference method. Here, we have presented some exclusive exotic propagation properties of Dirac delta potential that cannot be observed for other very similar potentials such as one-dimensional coulomb potential. We can now rectify any number of colliding wave packets provided that the correct parameters adjustment is possible. We have also addressed the wave packet speed control, wave packet splitting, wave packet rectification through collision process, wave packet dispersion, etc. The effects of different parameters such as the nonlinearity, fractitionality, dispersion, etc. on the wave packet-delta potential collision are also considered.
By propagating the many-body Schr\"odinger equation, we determine the exact time-dependent Kohn-Sham potential for a system of strongly correlated electrons which undergo field-induced tunneling. Numerous features are entirely absent from the approximations commonly used in time-dependent density-functional theory. The self-interaction correction is strong and time dependent, owing to electron localization, and prominent dynamic spatial potential steps arise from minima in the charge density, as modified by the Coulomb interaction experienced by the partially tunneled electron.