Bound-state spectrum of the hydrogen atom in strong magnetic fields

Energies of the bound states of the hydrogen atom in a uniform magnetic field are calculated for field strengths greater or equal to $B_0\approx 2.35\times {10}^9$ G. The convergent behavior of the quantum excesses (negative quantum defects) makes it possible to determine completely the bound-state spectrum for given values of the field strength $B$ and the azimuthal quantum number $m$. For $\mathrm{}\left|m\right|=0,1, \mathrm{and} 2$ results are presented which determine to a uniform relative accuracy of at least 0.1% the energies of all bound states for arbitrary field strengths from $\frac{B}{B_0}=1\mathrm{}$ to $\frac{B}{B_0}=500\mathrm{}$ or higher, beyond which the adiabatic approximation is of comparable accuracy.