  Spectra of $q \bar{q}$ hadrons are investigated in the framework of the
Hamiltonian obtained from the relativistic path integral in external
homogeneous magnetic field. The spectra of all 12 spin-isospin s-wave states,
generated by $\pi$ and $\rho$ mesons with different spin projections, are
studied both analytically and numerically on the lattice as functions of
(magnetic field) $eB$. Results are in agreement and demonstrate three types of
behavior, with characteristic splittings predicted by the theory.
