  This study addresses the effect of the magnetic hyperfine interaction on the
relativistic H1s wave functions. These are used to calculate the electric,
magnetic, and confinement force densities acting on the 1s electron. The
magnetic field couples Dirac equations for different angular momenta. These are
solved numerically for the hyperfine singlet and triplet, as well as for a
classical magnetic dipole. In the singlet ground state the hyperfine
interaction shifts the electron density toward the proton. A similar shift is
found for the classical dipole, and an opposite shift for the triplet. The
cross-over between charge accumulation and depletion occurs at 1.325 times the
Bohr radius. The behavior of the wave functions is investigated down to
distances smaller than the proton radius, including the incorporation of
virtual positrons. The force densities are determined and balanced against each
other.
