Figure 1

Relative difference $\mathrm{\Delta }=({\varrho }_D-{\varrho }_{\mathrm{FW}})/{\varrho }_D$ between the probability densities calculated from the wave functions in the Dirac and in the Foldy-Wouthuysen representations for $l=2,a=1,b=2i$. The difference is negligible for nonrelativistic electrons ($q_{\perp }=0.02,q_z=0.03$, lower curve) but it clearly becomes significant for relativistic electron beams ($q_{\perp }=0.5,q_z=1.0$, upper curve). The corresponding relativistic kinetic energy is $E-m{c}^2=250\mathrm{keV}$.