Hydrogen atoms in strong magnetic fields

We propose a variational scheme for calculating the energy eigenvalues and eigenfunctions of the hydrogen atom in the presence of a strong magnetic field. Numerical calculations were performed for several of the lowest states, and for the wavelengths of some allowed transitions. We discuss briefly the equivalence of the problems related with solid-state physics and astrophysics, and compare our results with previous calculations. Because the suggested scheme converges very fast for fields up to approximately ${10}^9$ G this is a convenient manner in which to treat problems where the interest is concentrated in the range of variation of the magnetic field from zero up to approximately ${10}^9$ G.