  We present an analytic approach to solving 1+1 dimensional QCD with an
adjoint Majorana fermion. In the UV this theory is described by a trivial CFT
containing free fermions. The quasi-primary operators of this CFT lead to a
discrete basis of states which is useful for diagonalizing the Hamiltonian of
the full strongly interacting theory. Working at large-$N$, we find that the
decoupling of high scaling-dimension quasi-primary operators from the
low-energy spectrum occurs exponentially fast in their scaling-dimension. This
suggests a scheme, whereby, truncating the basis to operators of dimension
below $\Delta_{max}$, one can calculate the low-energy spectrum, parametrically
to an accuracy of $e^{-\Delta_{max}}$ (although the precise accuracy depends on
the state). Choosing $\Delta_{max} =9.5$ we find very good agreement with the
known spectrum obtained earlier by numerical DLCQ methods. Specifically, below
the first three-particle threshold, we are able to identify all six
single-particle bound-states, as well as several two-particle thresholds.
