On the asymptotic decay of L 2 -solutions of one-body Schrödinger equations in unbounded domains

Source abstract

Synopsis The asymptotic decay of L 2 -solutions of Schrödinger equations (-Δ+V)ψ=0 in Δ R = {x εR n ∣∣x∣=r>R} is investigated, where V ( x ) = V 1 ( r ) + V 2 ( x ) with V 1 → ∞ for r ↑∞ and with some ε > 0 for large r . Under additional assumptions on the decay of V 1 , pointwise upper bounds to |ψ |and lower bounds to the spherical average of ψ are given showing the same asymptotics for r → ∞. For the case V → const. > 0 for r → ℝ (investigated in [8] a simplified treatment is given.