The hydrogen atom in a strong constant magnetic field

We present a variational calculation of eigenvalues and eigenvectors of a hydrogen atom in presence of a strong constant magnetic field. The numerical method, which yields very accurate results for a large range of the magnetic field, is basically that used by two of us (1) for anharmonic oscillators. In order to apply this method, we find convenient to use parabolic coordinates, which make our problem similar to the one of a two-dimensional anharmonic oscillator. The main innovations of our method are: the basis vectors used (radial eigenfunctions of a two-dimensional harmonic oscillator) and the optimtzation procedure of the parameters of these vectors. (1) G. Schiffrer and D. Stanzial : 11 Nuovo Cimento B. 90. 74 (1985)