Wave Propagation through Sparse Potential Barriers
نویسنده
چکیده
We prove that 3-dimensional Schrödinger operator with slowly decaying sparse potential has an a.c. spectrum that fills R. A new kind of WKB asymptotics for Green’s function is obtained. The absence of positive eigenvalues is established as well. Consider the Schrödinger operator H = −∆+ V, x ∈ R (1) We are interested in studying the scattering properties of H for the slowly decaying potential V . The following conjecture is due to Barry Simon [19] Conjecture. If V (x) is such that
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