  The quantum hydrodynamic model for charged particle systems is extended to
the cases of non zero magnetic fields. In this way, quantum corrections to
magnetohydrodynamics are obtained starting from the quantum hydrodynamical
model with magnetic fields. The quantum magnetohydrodynamics model is analyzed
in the infinite conductivity limit. The conditions for equilibrium in ideal
quantum magnetohydrodynamics are established. Translationally invariant exact
equilibrium solutions are obtained in the case of the ideal quantum
magnetohydrodynamic model.
