Lower Bounds of Growth Order of Solutions of Schrodinger Equations with Homogeneous Potentials

where A is a positive constant and A is the Laplacian. There are many articles investigating this problem for the two-particle Schrodinger operator. In these cases the authors usually assume that q(x) tends to 0 as \x\ tends to co. However, here we turn our attention to the manyparticle Schrodinger operator, and so we assume that the potential q(x) is a homogeneous function of x of degree — 2y. For example, the potential of the Schrodinger operator of an atom (or ion) consisting of a nucleus with charge -\-Z and m electrons given by