We determine the semiclassical coherent-state propagator for a particle going through onedimensional evolution in a simple barrier potential. The described semiclassical method makes use of complex trajectories which, by its turn, enables the definition of (real) traversal times in the complexified phase space. We then discuss the behavior of this time for a wave packet whose average energy is below the barrier height. [S0031-9007(97)04310-X]
We compute the semiclassical coherent-state propagator for a particle moving in a one-dimensional box. In this semiclassical approach complex trajectories are stationary paths of the propagator's asymptotic expansion and play a fundamental role. A second semiclassical approximation is also introduced, which makes use of real trajectories only. An application to a seemingly simple system, the infinite well, is carried out completely for the diagonal elements, and a comparison is made among the three possible methods, those based on complex and real trajectories and the ''exact case'' that is determined by decomposing the propagator into its eigenstates. ͓S1050-2947͑96͒04908-6͔
Isotopic substitution, nuclear reaction analysis, and x-ray photoelectron spectroscopy were employed to show that oxygen-deficient hafnium ͑Hf͒ silicates trap hydrogen atoms. Based on this experimental observation, we used first-principles calculations to investigate the structure, energetics, and electronic properties of H interacting with O vacancies in a hafnium silicate model. We found that O vacancies close to a Si atom are energetically favored when compared to vacancies in HfO 2 -like regions, implying that close-to-Si O vacancies are more likely to occur. Trapping of two H atoms at a close-to-Si O vacancy passivates the vacancy-induced gap states. The first H interacts with neighboring Hf atoms, whereas the second H binds to the Si atom.
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