  The linearly polarized Gowdy $T^3$ model is paradigmatic for studying
technical and conceptual issues in the quest for a quantum theory of gravity
since, after a suitable and almost complete gauge fixing, it becomes an exactly
soluble midisuperspace model. Recently, a new quantization of the model,
possessing desired features such as a unitary implementation of the gauge group
and of the time evolution, has been put forward and proven to be essentially
unique. An appropriate setting for making contact with other approaches to
canonical quantum gravity is provided by the Schr\"odinger representation,
where states are functionals on the configuration space of the theory. Here we
construct this functional description, analyze the time evolution in this
context and show that it is also unitary when restricted to physical states,
i.e. states which are solutions to the remaining constraint of the theory.
