Quantum-wave evolution in a step potential barrier

Abstract

By using an exact solution to the time-dependent Schrödinger 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 {\it forerunner} associated with a non-tunneling process, which propagates in space at exactly the semiclassical group velocity. We show that the time of arrival of the maximum of the {\it 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 {\it forerunner}, and to analyze the role played by the time of arrival, $3^{-1/2}\tau$, found recently by Muga and Büttiker [Phys. Rev. A {\bf 62}, 023808 (2000)].

To be published in Phys. Rev. A (2002)

References in corpus (4)

• Time dependence of evanescent quantum waves
• Front Propagation in Evanescent Media
• Sources of quantum waves
• Exact relativistic time evolution for a step potential barrier

Cited by in corpus (8)

• Effect of a potential step or impurity on the Bose-Einstein condensate mean field
• Tunneling dynamics in relativistic and nonrelativistic wave equations
• Ultra-fast propagation of Schrödinger waves in absorbing media
• Simultaneous arrival of information in absorbing wave guides
• Zitterbewegung and Klein-tunneling phenomena for transient quantum waves
• Above-Barrier Reflection of Cold Atoms by Resonant Laser Light within the Gross-Pitaevskii Approximation
• Transmission resonances in above-barrier reflection of ultra-cold atoms by the Rosen-Morse potential
• Dynamics of a quantum wave emitted by a decaying and evanescent point source