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Multidimensional periodic Schrödinger operator [electronic resource] : perturbation theory and applications

자료유형

E-Book(소장)

개인저자

Veliev, Oktay.

서명 / 저자사항

Multidimensional periodic Schrödinger operator [electronic resource] : perturbation theory and applications / Oktay Veliev.

발행사항

Cham : Springer International Publishing : Imprint: Springer, 2015.

형태사항

1 online resource(x, 242 p.).

총서사항

Springer tracts in modern physics,0081-3869, 1615-0430 (electronic) ; 263

ISBN

9783319166438

요약

The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given.

일반주기

Title from e-Book title page.

내용주기

Preface -- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- Constructive Determination of the Spectral Invariants -- Periodic Potential from the Spectral Invariants -- Conclusions.

서지주기

Includes bibliographical references and index.

이용가능한 다른형태자료

Issued also as a book.

일반주제명

Schrödinger operator. Perturbation (Mathematics). Spectral theory (Mathematics).

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008		200702s2015 sz ob 001 0 eng d
020		▼a 9783319166438
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082	0 4	▼a 530.12/4 ▼2 23
084		▼a 530.124 ▼2 DDCK
090		▼a 530.124
100	1	▼a Veliev, Oktay.
245	1 0	▼a Multidimensional periodic Schrödinger operator ▼h [electronic resource] : ▼b perturbation theory and applications / ▼c Oktay Veliev.
260		▼a Cham : ▼b Springer International Publishing : ▼b Imprint: Springer, ▼c 2015.
300		▼a 1 online resource(x, 242 p.).
490	1	▼a Springer tracts in modern physics, ▼x 0081-3869, ▼x 1615-0430 (electronic) ; ▼v 263
500		▼a Title from e-Book title page.
504		▼a Includes bibliographical references and index.
505	0	▼a Preface -- Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- Constructive Determination of the Spectral Invariants -- Periodic Potential from the Spectral Invariants -- Conclusions.
520		▼a The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given.
530		▼a Issued also as a book.
538		▼a Mode of access: World Wide Web.
650	0	▼a Schrödinger operator.
650	0	▼a Perturbation (Mathematics).
650	0	▼a Spectral theory (Mathematics).
830	0	▼a Springer tracts in modern physics ; ▼v 263.
856	4 0	▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-319-16643-8
945		▼a KLPA
991		▼a E-Book(소장)

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중앙도서관

No.	소장처	청구기호	등록번호	도서상태	반납예정일	예약	서비스
No. 1	소장처 중앙도서관/e-Book 컬렉션/	청구기호 CR 530.124	등록번호 E14027364	도서상태 대출불가(열람가능)	반납예정일	예약	서비스 M

Multidimensional periodic Schrödinger operator [electronic resource] : perturbation theory and applications

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