Three-dimensional hydrogen atom in crossed magnetic and electric fields

We give a solution of the three-dimensional Schr\"odinger equation for the electron of a hydrogen atom in external electric and magnetic fields of arbitrary mutual orientation. The rearrangement of the energy spectrum due to changing in the mutual orientation of the fields is evaluated by using the n=2 multiplet as an example. The calculations agree with second-order perturbation formulas that exist for the special cases of mutually parallel and orthogonal fields. For another special two-dimensional case which is currently being extensively investigated, namely, the hydrogen atom in a strong magnetic field, our approach agrees with calculations by other authors and yields more accurate binding energies for certain low-lying excited states that have been considered.