A detailed study of the lowest states 1 s _ { 0 } , 2 p _ { -1 } , 2 p _ { 0 } of the hydrogen atom placed in a magnetic field B \in ( 0 - 4.414 \times 10 ^ { 13 } { G } ) and their electromagnetic transitions ( 1 s _ { 0 } \leftrightarrow 2 p _ { -1 } and 1 s _ { 0 } \leftrightarrow 2 p _ { 0 } ) is carried out in the Born Oppenheimer approximation .
The variational method is used with a physically motivated recipe to design simple trial functions applicable to the whole domain of magnetic fields .
We show that the proposed functions yield very accurate results for the ionization ( binding ) energies .
Dipole and oscillator strengths are in good agreement with results by Ruder et al . ( ( 10 ) ) although we observe deviations up to \sim 30 \% for the oscillator strength of the ( linearly polarized ) electromagnetic transition 1 s _ { 0 } \leftrightarrow 2 p _ { 0 } at strong magnetic fields B \gtrsim 1000 a.u .