Multidimensional periodic Schrödinger operator : perturbation theory and applications /: perturbation theory and applications. ([2019])

• Record Type: Book
• Further Information: Note: Oktay Veliev.
• Authors: Veliev, Oktay
• Contents: Intro; Preface; Contents; 1 Preliminary Facts; 1.1 Lattices, Brillouin Zones, and Periodic Functions in mathbbRd; 1.2 Schrödinger Operator, Bloch Functions; 1.3 Band Structure, Fermi Surfaces, and Perturbations; 1.4 Some Discussions of the Perturbation Theory; References; 2 From One-Dimensional to Multidimensional; 2.1 Introduction; 2.2 Asymptotic Formulas for Eigenvalues in Two- and Three-Dimensional Cases; 2.2.1 On the Iterations of (2.1.10); 2.2.2 Asymptotic Formulas for the Non-resonance Eigenvalues; 2.2.3 Single Resonance Eigenvalues and Matrices 2.2.4 Estimations of the Resonance and Non-resonance Sets2.3 Simple Sets and Bloch Functions in Dimensions Two and Three; 2.3.1 Discussion of the Simplicity and the Asymptotic Formulas for the Bloch Functions; 2.3.2 Precise Construction of the Simple Set in the Dimension Two; 2.3.3 Precise Construction of the Simple Set in the Dimension Three; 2.4 Estimations of the Simple Sets and Isoenergetic Surfaces; 2.4.1 Some Properties of the Sets (2.4.7) and Their Applications; 2.4.2 The Proof of the Main Theorems; 2.4.3 The Proofs of the Estimations (2.4.18), (2.4.21), (2.4.23), and (2.4.24) 2.5 On the Nonsmooth Potentials2.5.1 Bloch Eigenvalues for the Nonsmooth Potentials; 2.5.2 Bloch Functions for the Nonsmooth Potentials; 2.5.3 Estimations of the Simple Sets for the Nonsmooth Potentials; References; 3 Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions; 3.1 Introduction; 3.2 Asymptotic Formulae for the Eigenvalues; 3.3 Bloch Eigenvalues Near the Diffraction Planes; 3.4 Asymptotic Formulas for the Bloch Functions; 3.5 Simple Sets and Isoenergetic Surfaces; 3.6 Bloch Functions Near the Diffraction Hyperplanes; References 4 Constructive Determination of the Spectral Invariants4.1 Introduction and Preliminary Facts; 4.2 First and Second Terms of the Asymptotics; 4.3 On the Derivatives of the Band Functions; 4.4 The Construction of the Spectral Invariants; 4.5 Appendices; References; 5 Periodic Potential from the Spectral Invariants; 5.1 Introduction; 5.2 On the Simple Invariants; 5.3 Finding the Fourier Coefficients Corresponding to the Boundary; 5.4 Inverse Problem in a Dense Set; 5.5 Finding the Simple Potential from the Invariants; 5.6 On the Stability of the Algorithm; 5.7 Uniqueness Theorems; References
• Edition: Second edition
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 530.12/4; Schrödinger operator; Perturbation (Mathematics); Spectral theory (Mathematics); Perturbation (Mathematics); Schrödinger operator; Spectral theory (Mathematics); Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030245788; 3030245780
• Notes: Note: Includes bibliographical references and index.; Note: Description based on online resource; title from digital title page (viewed on September 13, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.