Finite Gap Potentials and WKB Asymptotics¶for One-Dimensional Schrödinger Operators

被引：0

作者：

Thomas Kriecherbauer

Christian Remling

机构：

[1] Universität München,

[2] Mathematisches Institut,undefined

[3] Theresienstr. 39,undefined

[4] 80333 München,undefined

[5] Germany.¶E-mail: tkriech@rz.mathematik.uni-muenchen.de,undefined

[6] Universität Osnabrück,undefined

[7] Fachbereich Mathematik/Informatik,undefined

[8] 49069 Osnabrück,undefined

[9] Germany.¶E-mail: cremling@mathematik.uni-osnabrueck.de,undefined

来源：

Communications in Mathematical Physics | 2001年 / 223卷

关键词：

Riemann Surface; Potential Versus; Inversion Problem; Pointwise Bound; Hyperelliptic Riemann Surface;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Consider the Schrödinger operator H=−d2/dx2+V(x) with power-decaying potential V(x)=O(x−α). We prove that a previously obtained dimensional bound on exceptional sets of the WKB method is sharp in its whole range of validity. The construction relies on pointwise bounds on finite gap potentials. These bounds are obtained by an analysis of the Jacobi inversion problem on hyperelliptic Riemann surfaces.

引用

页码：409 / 435

页数：26

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