  In a preceding paper we introduced a formalism to study the scattering of low
intensity fields from a system of multi-level emitters embedded in a $3$D
dielectric medium. Here we show how this photon-scattering relation can be used
to analyze the scattering of single photons and weak coherent states from any
generic multi-level quantum emitter coupled to a $1$D waveguide. The reduction
of the photon-scattering relation to $1$D waveguides provides for the first
time a direct solution of the scattering problem involving low intensity fields
in the waveguide QED regime. To show how our formalism works, we consider
examples of multi-level emitters and evaluate the transmitted and reflected
field amplitude. Furthermore, we extend our study to include the dynamical
response of the emitters for scattering of a weak coherent photon pulse. As our
photon-scattering relation is based on the Heisenberg picture, it is quite
useful for problems involving photo-detection in the waveguide architecture. We
show this by considering a specific problem of state generation by
photo-detection in a multi-level emitter, where our formalism exhibits its full
potential. Since the considered emitters are generic, the $1$D results apply to
a plethora of physical systems like atoms, ions, quantum dots, superconducting
qubits, and nitrogen-vacancy centers coupled to a $1$D waveguide or
transmission line.
