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http://hdl.handle.net/11154/1797
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Title: | Quantum-wave evolution in a step potential barrier |
Authors: | Villavicencio, J Romo, R Silva, SSY |
Issue Date: | 2002 |
Abstract: | By using an exact solution to the time-dependent Schrodinger equation with a point source initial condition, we investigate both the time and spatial dependence of quantum waves in a step potential barrier. We find that for a source with energy below the barrier height, and for distances larger than the penetration length, the probability density exhibits a forerunner associated with a nontunneling process, which propagates in space at exactly the semiclassical group velocity. We show that the time of arrival of the maximum of the forerunner at a given fixed position inside the potential is exactly the traversal time tau. We also show that the spatial evolution of this transient pulse exhibits an invariant behavior under a rescaling process. This analytic property is used to characterize the evolution of the forerunner, and to analyze the role played by the time of arrival 3(-1/2)tau found recently by Muga and Buttiker [Phys. Rev. A 62, 023808 (2000)]. |
URI: | http://hdl.handle.net/11154/1797 |
ISSN: | 1050-2947 |
Appears in Collections: | Ciencias
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