  In this paper we investigate $1/N$ corrections to mesonic spectrum in
$1+1$-dimensional Quantum Chromodynamics ($\text{QCD}_2$) with fundamental
quarks using effective Hamiltonian method. We express the corrections in terms
of 't Hooft equation solutions. First, we consider 2-flavor model with a heavy
and a light quark. We show that, in contrast to some claims in earlier
literature, the $1/N$ correction to the mass of the heavy-light meson remains
finite when the light quark mass is taken to zero. Nevertheless, the
corrections become significantly larger in this limit; we attribute this to the
presence of massless modes in the spectrum. We also study the corrections to
the lightest meson mass in 1-flavor model and show that they are consistent
with recent numerical data, but not with the prediction coming from
bosonization. Then we study low energy effective theory for 2 flavors. We show
that the 3-meson interaction vertex correctly reproduces Wess-Zumino-Witten
(WZW) coupling when both quarks become massless. This coupling does not change
even if one of the quarks is massive. We employ Discretized Light Cone
Quatization (DLCQ) to check the continuum results and show that the improved
version can be used for small quark mass. Finally, we study the states
associated with $1\to 2$ meson thresholds. Using degenerate perturbation
theory, we show that when the decay is allowed by parity, the infinite $N$
theory has near-threshold bound states that mix one- and two-meson parts. They
are $1/3$ two-meson and $2/3$ one-meson and the corrections to their masses
have unusual scaling $\sim 1/N^{2/3}$.
