WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Christ, M; Kiselev, A

Published Date

  • February 1, 2001

Published In

Volume / Issue

  • 179 / 2

Start / End Page

  • 426 - 447

International Standard Serial Number (ISSN)

  • 0022-1236

Digital Object Identifier (DOI)

  • 10.1006/jfan.2000.3688

Citation Source

  • Scopus