  We study the problem of a temporal discontinuity in the permittivity of an
unbounded medium with Lorentzian dispersion. More specifically, we tackle the
situation in which a monochromatic plane wave forward-travelling in a
(generally lossy) Lorentzian-like medium scatters from the temporal "half-space
interface" that results from an abrupt temporal change in its plasma frequency
(while keeping its resonance frequency constant). In order to achieve momentum
preservation across the temporal discontinuity, we show how, unlike in the
well-known problem of a nondispersive discontinuity, the second-order nature of
the dielectric function now gives rise to two shifted frequencies. As a
consequence, whereas in the nondispersive scenario the continuity of the
electric displacement D and the magnetic induction B suffice to find the
amplitude of the new forward and backward wave, we now need two extra temporal
boundary conditions. That is, two forward and two backward plane waves are now
instantaneously generated in response to a forward-only plane wave. We also
include a transmission-line equivalent with lumped circuit elements that
describes the dispersive time-discontinuous scenario under consideration.
