  The influence of Lorentz- and CPT-violating terms (in "vector" and "axial
vector" couplings) on the Dirac equation is explicitly analyzed: plane wave
solutions, dispersion relations and eigenenergies are explicitly obtained. The
non-relativistic limit is worked out and the Lorentz-violating Hamiltonian
identified in both cases, in full agreement with the results already
established in the literature. Finally, the physical implications of this
Hamiltonian on the spectrum of hydrogen are evaluated both in the absence and
presence of a magnetic external field. It is observed that the fixed
background, when considered in a vector coupling, yields no qualitative
modification in the hydrogen spectrum, whereas it does provide an effective
Zeeman-like splitting of the spectral lines whenever coupled in the axial
vector form. It is also argued that the presence of an external fixed field
does not imply new modifications on the spectrum.
