Physics – Quantum Physics
Scientific paper
2008-08-05
American Journal of Physics 79(12): 1218-1231 (2011)
Physics
Quantum Physics
32 pages LaTeX, 8 figures
Scientific paper
10.1119/1.3636408
This article concerns a phenomenon of elementary quantum mechanics that is quite counter-intuitive, very non-classical, and apparently not widely known: a quantum particle can get reflected at a downward potential step. In contrast, classical particles get reflected only at upward steps. The conditions for this effect are that the wave length is much greater than the width of the potential step and the kinetic energy of the particle is much smaller than the depth of the potential step. This phenomenon is suggested by non-normalizable solutions to the time-independent Schroedinger equation, and we present evidence, numerical and mathematical, that it is also indeed predicted by the time-dependent Schroedinger equation. Furthermore, this paradoxical reflection effect suggests, and we confirm mathematically, that a quantum particle can be trapped for a long time (though not forever) in a region surrounded by downward potential steps, that is, on a plateau.
Garrido Pedro L.
Goldstein Sheldon
Lukkarinen Jani
Tumulka Roderich
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