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 O(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 authors solve the coupled Landau channel equations in a region extending well into the regime of overlapping Landau manifolds. Approximate level crossings are caused on the low-field side by the approximate separability of the Schrodinger equation and on the high-field side by interference between Landau channels. 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. The authors can also follow some states which, if they pass all approximate level crossings diabatically, evolve into Landau excited resonant states in the high-field regime.