Spectrum and continuum eigenfunctions of Schrödinger operators

We consider Schrödinger operators $\text{H = ?}\text{1}\text{2}\text{Δ + V}$ for a large class of potentials. V. We show that if H? = E? has a polynomially bounded solution ? then E is in the spectrum of H. This is accomplished by proving that the spectrum of H as an operator on L² is identical to its spectrum as an operator on the weighted L² space, L²_δ.