  In this paper, we have solved the de Sitter special relativistic
($\mathcal{SR}_{cR}$-) Dirac equation of hydrogen in the earth-QSO(quasar)
framework reference by means of the adiabatic approach. The aspects of geometry
effects of de Sitter space-time described by Beltrami metric are explored and
taken into account. It is found that the $\mathcal{SR}_{cR}$-Dirac equation of
hydrogen is a time dependent quantum Hamiltonian system. We provide an explicit
calculation to justify the adiabatic approach in dealing with this
time-dependent system. Since the radius of de Sitter sphere $R$ is
cosmologically large, the evolution of the system is very slow so that the
adiabatic approximation legitimately works with high accuracy. We conclude that
the electromagnetic fine-structure constant, the electron mass and the Planck
constant are time variations. This prediction of fine-structure constant is
consistent with the presently available observation data. For confirming it
further, experiments/observations are required.
