Accurate WKB Approximation for a 1D Problem with Low Regularity

Nier, F.

Serdica Mathematical Journal (2008)

  • Volume: 34, Issue: 1, page 113-126
  • ISSN: 1310-6600

Abstract

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2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of the boundary conditions brings also some interesting subtleties which require a careful application of Carleman’s method.

How to cite

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Nier, F.. "Accurate WKB Approximation for a 1D Problem with Low Regularity." Serdica Mathematical Journal 34.1 (2008): 113-126. <http://eudml.org/doc/281422>.

@article{Nier2008,
abstract = {2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of the boundary conditions brings also some interesting subtleties which require a careful application of Carleman’s method.},
author = {Nier, F.},
journal = {Serdica Mathematical Journal},
keywords = {WKB Method; Low Regularity; WKB method; low regularity},
language = {eng},
number = {1},
pages = {113-126},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Accurate WKB Approximation for a 1D Problem with Low Regularity},
url = {http://eudml.org/doc/281422},
volume = {34},
year = {2008},
}

TY - JOUR
AU - Nier, F.
TI - Accurate WKB Approximation for a 1D Problem with Low Regularity
JO - Serdica Mathematical Journal
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 34
IS - 1
SP - 113
EP - 126
AB - 2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.This article is concerned with the analysis of the WKB expansion in a classically forbidden region for a one dimensional boundary value Schrodinger equation with a non smooth potential. The assumed regularity of the potential is the one coming from a non linear problem and seems to be the critical one for which a good exponential decay estimate can be proved for the first remainder term. The treatment of the boundary conditions brings also some interesting subtleties which require a careful application of Carleman’s method.
LA - eng
KW - WKB Method; Low Regularity; WKB method; low regularity
UR - http://eudml.org/doc/281422
ER -

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