[en] Let Ω_R = Rⁿinverse slantB_R, where n ≥ 3 and B_R = {x element of Rⁿ:vertical strokexvertical stroke ≤ R}. We investigate the asymptotics of real valued solutions ψ element of L²(Ω_R) of the Schroedinger equation (-Δ+V-E)ψ = 0, where E < 0 and V(x) → 0 for vertical strokexvertical stroke → ∞: Let D denote an unbounded nodal domain of ψ (i.e. a component of Ω_Rinverse slant{x:ψ(x) = 0}), and let S(r) = {y element of S^n-1:ry element of D} with S^n-1 the unit sphere in Rⁿ. Under suitable assumptions on V it is shown that for some γ > 0, limsub(r → ∞) inf r^γ ∫sub(S(r)) ψ²dσ / ∫sub(S^n-1) ψ²dσ > 0 and limsub(r → ∞) inf ln (Volume(D intersection B_r))/ln r ≥ (n+1)/2. Results of this type are already non-trivial for radial problems with ψ satisfying non-radial boundary conditions on dΩ_R or for excited states of the Hydrogen atom if one considers linear combinations of different l-waves. (orig.)