Wkb Asymptotic Behavior of Almost All Generalized Eigenfunctions for One-dimensional Schrödinger Operators with Slowly Decaying Potentials
نویسندگان
چکیده
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 ∈ L(R), and V2 is bounded from above with A = lim supx→∞ V (x), while V ′ 2(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.
منابع مشابه
One-dimensional Schrödinger Operators with Slowly Decaying Potentials: Spectra and Asymptotics or Baby Fourier Analysis Meets Toy Quantum Mechanics
1. Pre-Introduction 2 2. Introduction and background 2 3. Three (sample) principal results 5 4. A criterion for ac spectrum 6 5. Expansions for generalized eigenfunctions 9 6. WKB approximation 10 7. Transmission and reflection coefficients 11 8. Reduction and expansion 13 9. Maximal operators 14 10. Multilinear operators and maximal variants 18 11. Wave operators and time-dependent scattering ...
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