Heisenberg uncertainty relation for relativistic electrons

Abstract

The Heisenberg uncertainty relation is derived for relativistic electrons described by the Dirac equation. The standard nonrelativistic lower bound 3/2ℏ is attained only in the limit and the wave function that reproduces this value is singular. At the other end, in the ultrarelativistic limit, the bound is the same as that found before for photons.

Keywords

• uncertainty relations
• relativistic electrons
• Dirac equation