# Klein Paradox

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows the reflection and transmission coefficients for a Dirac particle with spin-up incident on a square barrier of variable height The energy of the particle is fixed at 1 unit ), but its mass is allowed to vary from 0 to . What we see is that the negative energy solutions of the Dirac equation become accessible on the barrier side, thus allowing both reflection and transmission coefficients to increase beyond 1: Klein's paradox! The phenomenon can be explained by particle-antiparticle pair creation at the potential barrier.

Contributed by: Niels Walet (February 2010)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

[1] O. Klein, "Die Reflexion von Elektronen an Einem Potentialsprung Nach der Relativistischen Dynamik von Dirac," *Z. Phys.*, 53(3-4), 1929 pp. 157–165.

[2] See any textbook on relativistic quantum mechanics.

[3] Wikipedia entry for Klein paradox.

## Permanent Citation

"Klein Paradox"

http://demonstrations.wolfram.com/KleinParadox/

Wolfram Demonstrations Project

Published: February 3 2010