Paradoxical Reflection in Quantum Mechanics

Abstract

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.

32 pages LaTeX, 8 figures

References in corpus (2)

• On the Time-Dependent Analysis of Gamow Decay
• Gamow vectors and Borel summability

Cited by in corpus (9)

• The use of the stationary phase method as a mathematical tool to determine the path of optical beams
• Two-dimensional simulation of quantum reflection
• The Child-Langmuir law in the quantum domain
• Double well potentials with a quantum moat barrier or a quantum wall barrier give rise to similar entangled wave functions
• Transversal symmetry breaking and axial spreading modification for Gaussian optical beams
• Scattering Problems via Real-time Wave Packet Scattering
• Calculating field emission currents in nanodiodes - a multi-group formalism with space charge and exchange-correlation effects
• Wave-Particle Duality in Classical Mechanics
• Detection Time Distribution Predicted Using Absorbing Boundary Conditions and Imaginary Potentials