Nonperturbative behavior of a hydrogen atom in a van der Waals field

The spectrum of the hydrogen atom perturbed by the generalized van der Waals interaction {Δ}V(x,y,z)={γ}(x²+y²+β²{z}²$) is analyzed with a nonperturbative method of global approximation on a subspace grid. Considerable deviation from the perturbation formulas and violation of the analytic spectrum, which the system exhibits in special cases of the dynamical symmetry {β}=1/2, 1, and 2, have already been found for the field strengths H={}8{γ}{~}10^-3 a.u. {~}10⁶ G, in the region {γ}n⁴{}1 (n{~}10).