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

Journal Article (Journal Article)

We prove the WKB asymptotic behavior of solutions of the differential equation -d u/dx +V(x)u=Eu for a.e. E>A where V=V +V , V ∈L (R), and V is bounded from above with A=limsup V(x), while V′ (x)∈L (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. 2 2 p p 1 2 1 2 x→∞ 2

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