  We solve the Wheeler DeWitt equation for the Taub models in closed form when
both a cosmological constant and an electromagnetic field are present. In doing
so, we examine the 'excited states' of the quantum Taub models with the
aforementioned matter sources, and prove the existence of a countably infinite
number of 'excited' states. Additionally, we prove the existence of multiple
asymptotic solutions to the Lorentzian signature Wheeler DeWitt equation using
the Taub analogues of the 'wormhole', and 'no boundary' solutions of its
Euclidean-signature Hamilton Jacobi equation; we also study their 'excited
states. In the end we investigate qualitatively how our matter sources affect
the behavior of our wave functions and argue how these effects within the
context of quantum cosmology point to how a primordial electromagnetic field
could have played a profound role in the early universe.
