Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial

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Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial. / Федотов, Александр Александрович.

In: St. Petersburg Mathematical Journal, Vol. 29, No. 2, 2018, p. 363-381.

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

BibTeX

@article{92e826a4abcf4d90b4aea9b18d737f99,

title = "Complex WKB method for a difference Schr{\"o}dinger equation with the potential being a trigonometric polynomial",

abstract = "The difference Schr{\"o}dinger equation ψ(z + h) + ψ(z - h) + v(z)ψ(z) = Eψ(z), z ∈ C, is considered; here h is a positive number, E is the spectral parameter, and v is a trigonometric polynomial. The asymptotics of its entire solutions is studied as h → 0.",

keywords = "Complex WKB method, Difference Schr{\"o}dinger equation, complex WKB method, Difference Schrodinger equation",

author = "Федотов, {Александр Александрович}",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary 34E20. Key words and phrases. Difference Schr{\"o}dinger equation, complex WKB method. Supported by RFBR (grant no. 17-01-00668-a) and by the “M{\"o}bius Contest”, a foundation for support of young scientists.",

year = "2018",

doi = "10.1090/spmj/1497",

language = "English",

volume = "29",

pages = "363--381",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "2",

}

RIS

TY - JOUR

T1 - Complex WKB method for a difference Schrödinger equation with the potential being a trigonometric polynomial

AU - Федотов, Александр Александрович

N1 - Funding Information: 2010 Mathematics Subject Classification. Primary 34E20. Key words and phrases. Difference Schrödinger equation, complex WKB method. Supported by RFBR (grant no. 17-01-00668-a) and by the “Möbius Contest”, a foundation for support of young scientists.

PY - 2018

Y1 - 2018

N2 - The difference Schrödinger equation ψ(z + h) + ψ(z - h) + v(z)ψ(z) = Eψ(z), z ∈ C, is considered; here h is a positive number, E is the spectral parameter, and v is a trigonometric polynomial. The asymptotics of its entire solutions is studied as h → 0.

AB - The difference Schrödinger equation ψ(z + h) + ψ(z - h) + v(z)ψ(z) = Eψ(z), z ∈ C, is considered; here h is a positive number, E is the spectral parameter, and v is a trigonometric polynomial. The asymptotics of its entire solutions is studied as h → 0.

KW - Complex WKB method

KW - Difference Schrödinger equation

KW - complex WKB method

KW - Difference Schrodinger equation

UR - http://www.scopus.com/inward/record.url?scp=85043488985&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/complex-wkb-method-difference-schr%C3%B6dinger-equation-potential-trigonometric-polynomial

U2 - 10.1090/spmj/1497

DO - 10.1090/spmj/1497

M3 - Article

VL - 29

SP - 363

EP - 381

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 19063694