  We analyze mesons in constant magnetic fields ($B$) within a non-relativistic
constituent quark model. Our quark model contains a harmonic oscillator type
confining potential, and we perturbatively treat short range correlations to
account for the spin-flavor energy splittings. We study both neutral and
charged mesons taking into account the internal quark dynamics. The neutral
states are labelled by two-dimensional momenta for magnetic translations, while
the charged states by two discrete indices related to angular momenta. For $B
\ll \Lambda_{\rm QCD}^2$ ($\Lambda_{\rm QCD} \sim 200$ MeV: the QCD scale), the
analyses proceed as in usual quark models, while special precautions are needed
for strong fields, $B \sim \Lambda_{QCD}^2$, especially when we treat short
range correlations such as the Fermi-Breit-Pauli interactions. We compute the
energy spectra of mesons up to energies of $\sim 2.5$ GeV and use them to
construct the meson resonance gas. Within the assumption that the constituent
quark masses are insensitive to magnetic fields, the phase space enhancement
for mesons significantly increases the entropy, assisting a transition from a
hadron gas to a quark gluon plasma. We confront our results with the lattice
data, finding reasonable agreement for the low-lying spectra and the entropy
density at low temperature less than $\sim 100$ MeV, but our results at higher
energy scale suffer from artifacts of our confining potential and
non-relativistic treatments.
