  We consider three distinct methods to compute the mass spectrum of gauge
theories in the Hamiltonian formalism: (1) correlation-function scheme, (2)
one-point-function scheme, and (3) dispersion-relation scheme. The first one
examines spatial correlation functions as we do in the conventional Euclidean
Monte Carlo simulations. The second one uses the boundary effect to efficiently
compute the mass spectrum. The third one constructs the excited states and fits
their energy using the dispersion relation with selecting quantum numbers. Each
method has its pros and cons, and we clarify such properties in their
applications to the mass spectrum for the 2-flavor massive Schwinger model at
$m/g=0.1$ and $\theta=0$ using the density-matrix renormalization group (DMRG).
We note that the multi-flavor Schwinger model at small mass $m$ is a strongly
coupled field theory even after the bosonizations, and thus it deserves to
perform the first-principles numerical calculations. All these methods mostly
agree and identify the stable particles, pions $\pi_a$ ($J^{PG}=1^{-+}$), sigma
meson $\sigma$ ($J^{PG}=0^{++}$), and eta meson $\eta$ ($J^{PG}=0^{--}$). In
particular, we find that the mass of $\sigma$ meson is lighter than twice the
pion mass, and thus $\sigma$ is stable against the decay process, $\sigma \to
\pi\pi$. This is consistent with the analytic prediction using the WKB
approximation, and, remarkably, our numerical results are so close to the
WKB-based formula between the pion and sigma-meson masses,
$M_\sigma/M_\pi=\sqrt{3}$.
