Related Experiment Video
Updated: Dec 2, 2025

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics
Published on: January 19, 2018
Klein paradox for bosons, wave packets and negative tunnelling times
X Gutiérrez de la Cal1, M Alkhateeb2, M Pons3
1Departamento de Química-Física, Universidad del País Vasco, UPV/EHU, Leioa, Spain.
Abstract:
We analyse a little known aspect of the Klein paradox. A Klein-Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism is demonstrably acausal, yet an attempt to construct the corresponding causal solution of the Klein-Gordon equation fails. We relate the causal solution to a divergent multiple-reflections series, and show that the problem is remedied for a smooth barrier, where pair production at the energy equal to a half of the barrier's height is enhanced yet remains finite.
Related Concept Videos
The de Broglie Wavelength
The Uncertainty Principle
The Bohr Model
The Pauli Exclusion Principle
The Quantum-Mechanical Model of an Atom
Interference and Diffraction

