Hydrogen atom in combined electric and magnetic fields with arbitrary mutual orientations

For the hydrogen atom in combined magnetic and electric fields we investigate the dependence of the quantum spectra, classical dynamics, and statistical distributions of energy levels on the mutual orientation of the two external fields. Resonance energies and oscillator strengths are obtained by exact diagonalization of the Hamiltonian in a complete basis set, even far above the ionization threshold. At high excitation energies around the Stark saddle point the eigenenergies exhibit strong level repulsions when the angle between the fields is varied. The large avoided crossings occur between states with the same approximately conserved principal quantum number, $n,$ and this intramanifold mixing of states cannot be explained, not even qualitatively, by conventional perturbation theory. However, it is well reproduced by an extended perturbation theory, which takes into account all couplings between the angular momentum and Runge-Lenz vector. The large avoided crossings are interpreted as a quantum manifestation of classical intramanifold chaos. This interpretation is supported by both classical Poincaré surfaces of section, which reveal a mixed regular-chaotic intramanifold dynamics, and the statistical analysis of nearest-neighbor-spacing distributions.