WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials
We prove the WKB asymptotic behavior of solutions of the differential equation -d2u/dx2+V(x)u=Eu for a.e. E>A where V=V1+V2, V1∈Lp(R), and V2 is bounded from above with A=limsupx→∞V(x), while V′2(x)∈Lp(R), 1≤p<2. These results imply that Schrödinger operators with such potentials have absolutely continuous spectrum on (A, ∞). We also establish WKB asymptotic behavior of solutions for some energy-dependent potentials. © 2001 Academic Press.
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