Electron Scattering at a Soft Temporal Potential Step

We solve the problem of electron scattering at a soft temporal potential step. Given the relativistic nature of the problem, we use the Dirac equation, with its spinor wavefunction. We find solutions in terms of hypergeometric functions, which demonstrate that the observed phenomenon of later forward-wave and backward-wave electron scattering previously reported for a sharp (Heaviside) temporal potential step can be obtained experimentally and applied to new electronic devices.