  We develop a compact theory that can be applied to a variety of time-varying
dispersive materials. The continuous wave reflection and transmission
coefficients are replaced with equivalent operator expressions. In addition to
comparing this approach to existing numerical and analytical techniques, we
find that the eigenfunctions of these operators represent pulses that do not
change their spectra after interaction with the time-varying, dispersive
material. In addition, the poles of these operators represent the non-time
harmonic bound states of the system.
