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WKB and Spectral Analysis¶of One-Dimensional Schrödinger Operators¶with Slowly Varying Potentials

✍ Scribed by Michael Christ; Alexander Kiselev

Publisher
Springer
Year
2001
Tongue
English
Weight
144 KB
Volume
218
Category
Article
ISSN
0010-3616

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📜 SIMILAR VOLUMES

WKB Asymptotic Behavior of Almost All Ge
WKB Asymptotic Behavior of Almost All Generalized Eigenfunctions for One-Dimensional Schrödinger Operators with Slowly Decaying Potentials
✍ Michael Christ; Alexander Kiselev 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 192 KB

We prove the WKB asymptotic behavior of solutions of the differential equation &d 2 uÂdx 2 +V(x) u=Eu for a.e. E>A where V=V 1 +V 2 , V 1 # L p (R), and V 2 is bounded from above with A=lim sup x Ä V(x), while V$ 2 (x) # L p (R), 1 p<2. These results imply that Schro dinger operators with such poten