Inverse scattering theory and trace formulae for one-dimensional Schrodinger problems with singular potentials

被引：2

作者：

Rutkevich, S. B. ^{[1
]}

Diehl, H. W. ^{[1
]}

机构：

[1] Univ Duisburg Essen, Fak Phys, D-47048 Duisburg, Germany

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2015年 / 48卷 / 37期

关键词：

inverse scattering theory; trace formulae; singular Schrodinger operator; DIFFERENTIAL-OPERATORS; CRITICAL BEHAVIOR; SYSTEM; MODEL;

D O I：

10.1088/1751-8113/48/37/375201

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Inverse scattering theory is extended to one-dimensional Schrodinger problems with near-boundary singularities of the form v(z -> 0)similar or equal to-z(-2/4) + v(-1) z(-1). Trace formulae relating the boundary value v0 of the nonsingular part of the potential to spectral data are derived. Their potential is illustrated by applying them to a number of Schrodinger problems with singular potentials.

引用

页数：25

共 36 条

[1] [Anonymous], APPL MATH SERIES
[2] [Anonymous], 1989, TEXTS MONOGRAPHS PHY
[3] [Anonymous], 1960, DOKL AKAD NAUK SSSR+
[4] CRITICAL BEHAVIOR OF SEMI-INFINITE SYSTEMS
BRAY, AJ
MOORE, MA
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1977, 10 (11): : 1927 - 1962
[5] CRITICAL BEHAVIOR OF A SEMI-INFINITE SYSTEM - N-VECTOR MODEL IN LARGE-N LIMIT
BRAY, AJ
MOORE, MA
[J]. PHYSICAL REVIEW LETTERS, 1977, 38 (14) : 735 - 738
[6] Chadan K., 1997, An Introduction to Inverse Scattering and Inverse Spectral Problems, P131, DOI [10.1137/1.9780898719710.ch4, DOI 10.1137/1.9780898719710.CH4]
[7] The trigonometric Rosen-Morse potential in the supersymmetric quantum mechanics and its exact solutions
Compean, CB
Kirchbach, M
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (03): : 547 - 557
[8] Comment on "Casimir force in the O(n → ∞) model with free boundary conditions"
Diehl, H. W.
Grueneberg, Daniel
Hasenbusch, Martin
Hucht, Alfred
Rutkevich, Sergei B.
Schmidt, Felix M.
[J]. PHYSICAL REVIEW E, 2015, 91 (02):
[9] 0 Large-n approach to thermodynamic Casimir effects in slabs with free surfaces
Diehl, H. W.
Grueneberg, Daniel
Hasenbusch, Martin
Hucht, Alfred
Rutkevich, Sergei B.
Schmidt, Felix M.
[J]. PHYSICAL REVIEW E, 2014, 89 (06):
[10] The O(n) φ4 model with free surfaces in the large-n limit: some exact results for boundary critical behaviour, fluctuation-induced forces and distant-wall corrections
Diehl, H. W.
Rutkevich, S. B.
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (14)

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