Charged anisotropic harmonic oscillator and the hydrogen atom in crossed fields

We perform a gauge-independent pseudoseparation of the center-of-mass motion for neutral two-body systems in crossed fields. The resulting Hamiltonian is investigated for two different cases of the interaction. First, we reduce the Hamiltonian for a two-particle system with anisotropic harmonic interaction in a magnetic field to the Hamiltonian of a charged anisotropic harmonic oscillator in a magnetic field. For the latter we derive closed-form analytical expressions of its eigenenergies and wave functions. Second, we investigate the hydrogen atom in crossed fields. The potential for the relative motion of electron and proton exhibits an outer potential well at large distances. We perform extensive numerical calculations of a large number of eigenvalues and wave functions and compare these to the analytical results of a harmonic approximation of the potential well.