  We study the effect of a static homogeneous external magnetic field on
charmonium and bottomonium states. In an external magnetic field, quarkonium
states do not have a conserved center-of-mass momentum. Instead there is a new
conserved quantity called the pseudomomentum which takes into account the
Lorentz force on the particles in the system. When written in terms of the
pseudomomentum, the internal and center-of-mass motions do not decouple and, as
a result, the properties of quarkonia depend on the states' center-of-mass
momentum. We analyze the behavior of heavy particle-antiparticle pairs subject
to an external magnetic field assuming a three dimensional harmonic potential
and Cornell potential plus spin-spin interaction. In the case of the Cornell
potential, we also take into account the mixing of the eta_c and J/psi states
and eta_b and Upsilon states due to the background magnetic field. We then
numerically calculate the dependence of the masses and mixing fractions on the
magnitude of the background magnetic field and center-of-mass momentum of the
state.
