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  • 1
    Online Resource
    Online Resource
    Non-self-adjoint Schrödinger operator with a periodic potential (2021)
    Cham : Springer
    Details
    UID:
    gbv_1761802984
    Format: 1 Online-Ressource (X, 294 Seiten)
    ISBN: 9783030726836
    Series Statement: Springer eBook Collection
    Content: This book gives a complete spectral analysis of the non-self-adjoint Schrödinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schrödinger operator, the book features a complete spectral analysis of the Mathieu-Schrödinger operator and the Schrödinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.
    Note: 1. Spectral Theory for the Schrödinger Operator with a Complex-Valued Periodic Potential -- 2. On the Special Potentials -- 3. On the Matheiu-Schrödinger Operator -- 4. PT-Symmetric Periodic Optical Potential -- Index.
    Additional Edition: ISBN 9783030726829
    Additional Edition: Erscheint auch als Druck-Ausgabe Veliev, Oktay Non-self-adjoint Schrödinger operator with a periodic potential Cham : Springer Nature, 2021 ISBN 9783030726829
    Language: English
    Keywords: Hamilton-Operator ; Selbstadjungiertheit
    DOI: 10.1007/978-3-030-72683-6
    URL: lizenzpflichtig
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    UB Potsdam
  • 2
    Online Resource
    Online Resource
    Non-self-adjoint Schrödinger operator with a periodic potential / (2021)
    Cham, Switzerland :Springer,
    Details
    UID:
    almafu_9959888229602883
    Format: 1 online resource (301 pages)
    ISBN: 3-030-72683-5
    Note: Intro -- Preface -- Contents -- 1 Introduction and Overview -- 2 Spectral Theory for the Schrödinger Operator with a Complex-Valued Periodic Potential -- 2.1 Introduction -- 2.2 On the Floquet Theory and Spectrum of L(q) -- 2.3 Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- 2.3.1 Uniform Asymptotic Formulas for the Isolated Eigenvalues -- 2.3.2 Asymptotic Formulas for the Isolated Pairs -- 2.3.3 On the Numerations of the Bloch Eigenvalues and Bands -- 2.4 Spectral Singularities and ESS of the Operator L(q) -- 2.5 Spectral Expansion for the Non-self-adjoint Operator L(q) -- 2.6 The Necessity of the Brackets and P.V. Integrals and Criteria for the Elegant Expansion -- 2.7 On the Asymptotic Spectrality of L(q) -- 2.7.1 Spectral Singularities and Spectrality -- 2.7.2 On the Asymptotically Spectral Potentials -- 2.8 Appendices -- 3 On the Special Potentials -- 3.1 On the Even Potentials -- 3.2 On the PT-Symmetric Potentials -- 3.2.1 General Properties of the Spectrum -- 3.2.2 On the Bands Γn for Large n -- 3.2.3 Reality and Non-Reality of the Bands and Spectrality of L(q) -- 3.2.4 Finite Zone PT-Symmetric Periodic Potentials -- 3.2.5 Conclusions, Notes and References -- 3.3 Pure Complex-Valued Potentials with Pure Real Spectrum -- 3.3.1 On the Bloch Eigenvalues and Bloch Function -- 3.3.2 On the Inverse Problem -- 3.3.3 On the Spectral Singularities and ESS -- 4 On the Mathieu-Schrödinger Operator -- 4.1 Introduction -- 4.2 Asymptotic Formulas for the Isolated Eigenvalues and Isospectrality -- 4.3 Asymptotic Formulas for the Pairs of the Eigenvalues and Spectrality -- 4.4 On the ESS and Spectral Expansion of H(a,b) -- 4.5 On Simplicity of the Periodic and Antiperiodic Eigenvalues and Elegant Spectral Expansion -- 5 PT-Symmetric Periodic Optical Potential -- 5.1 Introduction -- 5.2 On the Bloch Eigenvalues. , 5.3 On the Bands and Components of the Spectrum -- 5.4 Spectral Singularities, ESS and Spectral Expansion -- 5.5 Finding the Second Critical Point -- 5.6 On the Small Perturbations -- 5.7 Conclusions and Notes -- Index.
    Additional Edition: ISBN 3-030-72682-7
    Language: English
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Charité
  • 3
    Online Resource
    Online Resource
    Non-self-adjoint Schrödinger operator with a periodic potential / (2021)
    Cham, Switzerland :Springer,
    Details
    UID:
    edoccha_9959888229602883
    Format: 1 online resource (301 pages)
    ISBN: 3-030-72683-5
    Note: Intro -- Preface -- Contents -- 1 Introduction and Overview -- 2 Spectral Theory for the Schrödinger Operator with a Complex-Valued Periodic Potential -- 2.1 Introduction -- 2.2 On the Floquet Theory and Spectrum of L(q) -- 2.3 Asymptotic Formulas for the Bloch Eigenvalues and Bloch Functions -- 2.3.1 Uniform Asymptotic Formulas for the Isolated Eigenvalues -- 2.3.2 Asymptotic Formulas for the Isolated Pairs -- 2.3.3 On the Numerations of the Bloch Eigenvalues and Bands -- 2.4 Spectral Singularities and ESS of the Operator L(q) -- 2.5 Spectral Expansion for the Non-self-adjoint Operator L(q) -- 2.6 The Necessity of the Brackets and P.V. Integrals and Criteria for the Elegant Expansion -- 2.7 On the Asymptotic Spectrality of L(q) -- 2.7.1 Spectral Singularities and Spectrality -- 2.7.2 On the Asymptotically Spectral Potentials -- 2.8 Appendices -- 3 On the Special Potentials -- 3.1 On the Even Potentials -- 3.2 On the PT-Symmetric Potentials -- 3.2.1 General Properties of the Spectrum -- 3.2.2 On the Bands Γn for Large n -- 3.2.3 Reality and Non-Reality of the Bands and Spectrality of L(q) -- 3.2.4 Finite Zone PT-Symmetric Periodic Potentials -- 3.2.5 Conclusions, Notes and References -- 3.3 Pure Complex-Valued Potentials with Pure Real Spectrum -- 3.3.1 On the Bloch Eigenvalues and Bloch Function -- 3.3.2 On the Inverse Problem -- 3.3.3 On the Spectral Singularities and ESS -- 4 On the Mathieu-Schrödinger Operator -- 4.1 Introduction -- 4.2 Asymptotic Formulas for the Isolated Eigenvalues and Isospectrality -- 4.3 Asymptotic Formulas for the Pairs of the Eigenvalues and Spectrality -- 4.4 On the ESS and Spectral Expansion of H(a,b) -- 4.5 On Simplicity of the Periodic and Antiperiodic Eigenvalues and Elegant Spectral Expansion -- 5 PT-Symmetric Periodic Optical Potential -- 5.1 Introduction -- 5.2 On the Bloch Eigenvalues. , 5.3 On the Bands and Components of the Spectrum -- 5.4 Spectral Singularities, ESS and Spectral Expansion -- 5.5 Finding the Second Critical Point -- 5.6 On the Small Perturbations -- 5.7 Conclusions and Notes -- Index.
    Additional Edition: ISBN 3-030-72682-7
    Language: English
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Charité
  • 4
    Online Resource
    Online Resource
    Non-self-adjoint Schrödinger Operator with a Periodic Potential (2021)
    Cham : Springer International Publishing | Cham : Springer
    Details
    UID:
    b3kat_BV047390405
    Format: 1 Online-Ressource (X, 294 p. 10 illus., 9 illus. in color)
    Edition: 1st ed. 2021
    ISBN: 9783030726836
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-72682-9
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-72684-3
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 978-3-030-72685-0
    Language: English
    DOI: 10.1007/978-3-030-72683-6
    URL: Volltext  (URL des Erstveröffentlichers)
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    Online Access
    Open Access Request
    TH Brandenburg
  • 5
    Online Resource
    Online Resource
    Non-self-adjoint Schrödinger Operator with a Periodic Potential (2021)
    Cham :Springer International Publishing :
    Details
    UID:
    almahu_9949083898102882
    Format: X, 294 p. 10 illus., 9 illus. in color. , online resource.
    Edition: 1st ed. 2021.
    ISBN: 9783030726836
    Content: This book gives a complete spectral analysis of the non-self-adjoint Schrödinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schrödinger operator, the book features a complete spectral analysis of the Mathieu-Schrödinger operator and the Schrödinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.
    Note: 1. Spectral Theory for the Schrödinger Operator with a Complex-Valued Periodic Potential -- 2. On the Special Potentials -- 3. On the Matheiu-Schrödinger Operator -- 4. PT-Symmetric Periodic Optical Potential -- Index.
    In: Springer Nature eBook
    Additional Edition: Printed edition: ISBN 9783030726829
    Additional Edition: Printed edition: ISBN 9783030726843
    Additional Edition: Printed edition: ISBN 9783030726850
    Language: English
    DOI: 10.1007/978-3-030-72683-6
    URL: https://doi.org/10.1007/978-3-030-72683-6
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    HU Berlin
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