Finite gap potentials and WKB asymptotics for one-dimensional Schrodinger operators

Authors
Kriecherbauer, T Remling, C
Citation
T. Kriecherbauer et C. Remling, Finite gap potentials and WKB asymptotics for one-dimensional Schrodinger operators, COMM MATH P, 223(2), 2001, pp. 409-435
Citations number
30
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
223
Issue
2
Year of publication
2001
Pages
409 - 435
Database
ISI
SICI code
0010-3616(200110)223:2<409:FGPAWA>2.0.ZU;2-U
Abstract
Consider the Schrodinger operator H = -d(2)/dx(2) + V(X) with power-decayin g potential V(x) = O(x(-alpha)). We prove that a previously obtained dimens ional bound on exceptional sets of the WKB method is sharp in its whole ran ge of validity. The construction relies on pointwise bounds:on finite gap p otentials. These bounds are obtained by an analysis of the Jacobi inversion problem on hyperelliptic Riemann surfaces.