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A note on the Schrödinger operator with a long-range potential. / Yafaev, D.R.

In: Letters in Mathematical Physics, Vol. 109, No. 12, 12.2019, p. 2625-2648.

Research output: Contribution to journal › Article › peer-review

Harvard

Yafaev, DR 2019, 'A note on the Schrödinger operator with a long-range potential', Letters in Mathematical Physics, vol. 109, no. 12, pp. 2625-2648. https://doi.org/10.1007/s11005-019-01200-z

APA

Yafaev, D. R. (2019). A note on the Schrödinger operator with a long-range potential. Letters in Mathematical Physics, 109(12), 2625-2648. https://doi.org/10.1007/s11005-019-01200-z

Vancouver

Yafaev DR. A note on the Schrödinger operator with a long-range potential. Letters in Mathematical Physics. 2019 Dec;109(12):2625-2648. https://doi.org/10.1007/s11005-019-01200-z

Author

Yafaev, D.R. / A note on the Schrödinger operator with a long-range potential. In: Letters in Mathematical Physics. 2019 ; Vol. 109, No. 12. pp. 2625-2648.

BibTeX

@article{cefa28ec99f14496bc778ea7533c6148,
title = "A note on the Schr{\"o}dinger operator with a long-range potential",
abstract = "Our goal is to develop spectral and scattering theories for the one-dimensional Schr{\"o}dinger operator with a long-range potential q(x), x≥ 0. Traditionally, this problem is studied with a help of the Green–Liouville approximation. This requires conditions on the first two derivatives q ′(x) and q ′ ′(x). We suggest a new Ansatz that allows us to develop a consistent theory under the only assumption q ′∈ L 1. ",
keywords = "Dimension one, Eigenfunction expansion, Limiting absorption principle, Modified Green–Liouville Ansatz, Schr{\"o}dinger equation",
author = "D.R. Yafaev",
note = "Yafaev, D.R. A note on the Schr{\"o}dinger operator with a long-range potential. Lett Math Phys 109, 2625–2648 (2019) doi:10.1007/s11005-019-01200-z",
year = "2019",
month = dec,
doi = "10.1007/s11005-019-01200-z",
language = "English",
volume = "109",
pages = "2625--2648",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer Nature",
number = "12",

}

RIS

TY - JOUR

T1 - A note on the Schrödinger operator with a long-range potential

AU - Yafaev, D.R.

N1 - Yafaev, D.R. A note on the Schrödinger operator with a long-range potential. Lett Math Phys 109, 2625–2648 (2019) doi:10.1007/s11005-019-01200-z

PY - 2019/12

Y1 - 2019/12

N2 - Our goal is to develop spectral and scattering theories for the one-dimensional Schrödinger operator with a long-range potential q(x), x≥ 0. Traditionally, this problem is studied with a help of the Green–Liouville approximation. This requires conditions on the first two derivatives q ′(x) and q ′ ′(x). We suggest a new Ansatz that allows us to develop a consistent theory under the only assumption q ′∈ L 1.

AB - Our goal is to develop spectral and scattering theories for the one-dimensional Schrödinger operator with a long-range potential q(x), x≥ 0. Traditionally, this problem is studied with a help of the Green–Liouville approximation. This requires conditions on the first two derivatives q ′(x) and q ′ ′(x). We suggest a new Ansatz that allows us to develop a consistent theory under the only assumption q ′∈ L 1.

KW - Dimension one

KW - Eigenfunction expansion

KW - Limiting absorption principle

KW - Modified Green–Liouville Ansatz

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85068992156&partnerID=8YFLogxK

U2 - 10.1007/s11005-019-01200-z

DO - 10.1007/s11005-019-01200-z

M3 - Article

VL - 109

SP - 2625

EP - 2648

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 12

ER -

ID: 36484288