On Two-Dimensional Above-Barrier Penetration and Sub-Barrier Tunneling for Non-Relativistic Particles and Photons

Vladislav S. Olkhovsky, Mariya V. Romaniuk

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DOI: 10.4236/jmp.2011.210145                

Abstract

We study the two-dimensional above-barrier penetration and the sub-barrier tunneling of non-relativistic particles and photons, described in the quasi-monochromatic approximation by simple plane waves. Our scheme represents the motion from the left free-motion zero-potential region to the right zero-potential region through the intermediate region with a one-dimensional rectangular potential barrier along the axis, normal to the both parallel interfaces between all three regions, and with the zero potential along the axis, parallel to the those interfaces. We have firstly obtained the analytical expressions for the infinite series of multiple internal and external reflections and also of multiple transmitted waves of particles and photons, with equal shifts between them along the interfaces for the above-barrier penetration and with various shifts between them in the case of the sub-barrier tunneling. Finally the Hartman and Fletcher effect for any transmitted wave is established.

Keywords

Two-Dimensional (2D) Penetration and Tunneling, Quasi-Monochromatic Approximation, Propagating Plane Waves, Evanescent and Anti-Evanescent Waves

Conflicts of Interest

The authors declare no conflicts of interest.

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