Resolution of the Klein Paradox

Electron scattering off a super-critical potential

The dynamics of the positron density (red) is animated. The data was obtained from second quantized three-particle wave function. The dip is the reduction due to the incoming electron colliding with the potential. For comparison we also show the solution corresponding to the reflected (blue) and "transmitted" (line) electron wave packet from an independent single-particle calculation. The initial electron is a Gaussian with an average energy of 5000 and a width of 0.03 . The super-critical potential is described by V(x)=0.5 V0 (1+tanh(x/W)) with V0= 2c^2+10^4 and W=0.3/c. Atomic units are adopted in this simulation. [P.Krekora, Q. Su and R. Grobe, Phys. Rev. Lett., in press.]