On Nodes of Local Solutions to Schrodinger Equations

Note that ψ ∈ C^∞(Ω) by elliptic regularity. Further let ∈ > 0, B_∈ {x ∈ ℝⁿ||x| > ∈} such that B_∈ ⊂ ß. In the following we present some recent results on the behaviour of the nodal set and the nodal domains of ψ in B _∈. Most of these results have just appeared in [9]. To prove some of these results we suitably adapt techniques which have been developed in [[7] to investigate the nodal behaviour of local solutions of Schrödinger equations in a neighbourhood of infinity. Those aspects just indicated in [[9] are given in detail here.