Relativistic Electron Wave Packets Carrying Angular Momentum

There are important differences between the nonrelativistic and relativistic description of electron beams. In the relativistic case the orbital angular momentum quantum number cannot be used to specify the wave functions and the structure of vortex lines in these two descriptions is completely different. We introduce analytic solutions of the Dirac equation in the form of exponential wave packets and we argue that they properly describe relativistic electron beams carrying angular momentum.

Figure 1

Normalized modulus $|\psi |$ of the wave function (15) as a function of $\rho /\mathrm{ƛ}$ plotted for $l=10$ and different values of the parameter $b$.

Figure 2

Normalized spectral functions $g_N(E)$ plotted for $l=10$ and different values of the parameter $b$.

Figure 3

Distribution of vorticity in the exponential beam.