  Waves in space-dependent and time-dependent materials obey similar wave
equations, with interchanged time- and space-coordinates. However, since the
causality conditions are the same in both types of material (i.e., without
interchangement of coordinates), the solutions are dissimilar.
  We present a systematic treatment of wave propagation and scattering in 1D
space-dependent and time-dependent materials. After formulating unified
equations, we discuss Green's functions and simple wave field representations
for both types of material. Next we discuss propagation invariants, i.e.,
quantities that are independent of the space coordinate in a space-dependent
material (such as the net power-flux density) or of the time coordinate in a
time-dependent material (such as the net field-momentum density). A discussion
of reciprocity theorems leads to the well-known source-receiver reciprocity
relation for the Green's function of a space-dependent material and a new
source-receiver reciprocity relation for the Green's function of a
time-dependent material. A discussion of general wave field representations
leads to the well-known expression for Green's function retrieval from the
correlation of passive measurements in a space-dependent material and a new
expression for Green's function retrieval in a time-dependent material.
  After an introduction of a matrix-vector wave equation, we discuss propagator
matrices for both types of material. Since the initial condition for a
propagator matrix in a time-dependent material follows from the boundary
condition for a propagator matrix in a space-dependent material by
interchanging the time- and space-coordinates, the propagator matrices for both
types of material are interrelated in the same way. This also applies to
representations and reciprocity theorems involving propagator matrices.
