Matching the low-field region and the high-field region for the hydrogen atom in a uniform magnetic field

The hydrogen atom in a uniform magnetic field is studied for arbitrary field strengths. Low-field calculations exploit the 0(4) supersymmetry of the field free H atom and proceed via diagonalisation of a reduced Hamiltonian in a complete basis. The calculations extend well into the n-mixing regime and include bound states near and above the zero-field ionisation threshold. On the high-field side, the coupled Landau channel equations are solved in a region extending well into the regime of overlapping Landau manifolds. Matching of the low-field results and the high-field results enables one to follow the evolution of bound states with effective quantum numbers less than 14 all the way from the zero-field case to the high-field limit. (author)