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The Resource PT-symmetric Schrödinger operators with unbounded potentials, Jan Nesemann

PT-symmetric Schrödinger operators with unbounded potentials, Jan Nesemann

Creator
Summary
Following the pioneering work of Carl M. Bender et al. (1998), there has been an increasing interest in theoretical physics in so-called PT-symmetric Schrödinger operators. In the physical literature, the existence of Schrödinger operators with PT-symmetric complex potentials having real spectrum was considered a surprise and many examples of such potentials were studied in the sequel. From a mathematical point of view, however, this is no surprise at all - provided one is familiar with the theory of self-adjoint operators in Krein spaces. Jan Nesemann studies relatively bounded perturbations of self-adjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively form-bounded perturbations and for pseudo-Friedrichs extensions. The author pays particular attention to the case when the unperturbed self-adjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum
Language
eng
Work
Publication
Extent
1 online resource
Contents
  • Acknowledgment; Table of Contents; Introduction; Chapter 1 Relatively Bounded Perturbations inKrein Spaces; 1.1 Linear Operators in Krein Spaces; 1.2 Stability Theorems; 1.2.1 Relatively Bounded and Relatively CompactOperators; 1.2.2 The Case of Relative Bound 0; 1.2.3 Stability of Self-Adjointness in Krein Spaces; 1.3 Continuity of Separated Parts of the Spectrum; 1.3.1 Continuity of Resolvents; 1.3.2 Perturbation of Isolated Parts of the Spectrum; 1.3.3 Perturbation of Spectra of Self-Adjoint Operatorsin Hilbert Spaces; 1.3.4 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces
  • Chapter 2 Relatively Form-BoundedPerturbations in Krein Spaces2.1 Stability Theorems; 2.1.1 Accretive and Sectorial Operators; 2.1.2 Quadratic Forms and Associated Operators; 2.1.3 Relatively Form-Bounded and Relatively Form-Compact Operators; 2.2 Continuity of Separated Parts of the Spectrum; 2.2.1 Perturbation of Spectra of Self-Adjoint Operatorsin Hilbert Spaces; 2.2.2 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces; 2.3 Pseudo-Friedrichs Extensions; 2.3.1 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces; Chapter 3Examples; 3.1 Example 1; 3.2 Example 2
Isbn
9783834817624
Instance
Label
PT-symmetric Schrödinger operators with unbounded potentials
Title
PT-symmetric Schrödinger operators with unbounded potentials
Statement of responsibility
Jan Nesemann
Creator
Subject
Language
eng
Summary
Following the pioneering work of Carl M. Bender et al. (1998), there has been an increasing interest in theoretical physics in so-called PT-symmetric Schrödinger operators. In the physical literature, the existence of Schrödinger operators with PT-symmetric complex potentials having real spectrum was considered a surprise and many examples of such potentials were studied in the sequel. From a mathematical point of view, however, this is no surprise at all - provided one is familiar with the theory of self-adjoint operators in Krein spaces. Jan Nesemann studies relatively bounded perturbations of self-adjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively form-bounded perturbations and for pseudo-Friedrichs extensions. The author pays particular attention to the case when the unperturbed self-adjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum
Cataloging source
HKP
http://library.link/vocab/creatorName
Nesemann, Jan
Dewey number
510
Index
no index present
Language note
English
LC call number
QA329
LC item number
.N47 2011eb
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/subjectName
  • Operator theory
  • Kreĭn spaces
  • Kreĭn spaces
  • Operator theory
Label
PT-symmetric Schrödinger operators with unbounded potentials, Jan Nesemann
Instantiates
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Acknowledgment; Table of Contents; Introduction; Chapter 1 Relatively Bounded Perturbations inKrein Spaces; 1.1 Linear Operators in Krein Spaces; 1.2 Stability Theorems; 1.2.1 Relatively Bounded and Relatively CompactOperators; 1.2.2 The Case of Relative Bound 0; 1.2.3 Stability of Self-Adjointness in Krein Spaces; 1.3 Continuity of Separated Parts of the Spectrum; 1.3.1 Continuity of Resolvents; 1.3.2 Perturbation of Isolated Parts of the Spectrum; 1.3.3 Perturbation of Spectra of Self-Adjoint Operatorsin Hilbert Spaces; 1.3.4 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces
  • Chapter 2 Relatively Form-BoundedPerturbations in Krein Spaces2.1 Stability Theorems; 2.1.1 Accretive and Sectorial Operators; 2.1.2 Quadratic Forms and Associated Operators; 2.1.3 Relatively Form-Bounded and Relatively Form-Compact Operators; 2.2 Continuity of Separated Parts of the Spectrum; 2.2.1 Perturbation of Spectra of Self-Adjoint Operatorsin Hilbert Spaces; 2.2.2 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces; 2.3 Pseudo-Friedrichs Extensions; 2.3.1 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces; Chapter 3Examples; 3.1 Example 1; 3.2 Example 2
Control code
756192733
Dimensions
unknown
Extent
1 online resource
Form of item
online
Isbn
9783834817624
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-8348-8327-8
Specific material designation
remote
System control number
(OCoLC)756192733
Label
PT-symmetric Schrödinger operators with unbounded potentials, Jan Nesemann
Publication
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
mixed
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Acknowledgment; Table of Contents; Introduction; Chapter 1 Relatively Bounded Perturbations inKrein Spaces; 1.1 Linear Operators in Krein Spaces; 1.2 Stability Theorems; 1.2.1 Relatively Bounded and Relatively CompactOperators; 1.2.2 The Case of Relative Bound 0; 1.2.3 Stability of Self-Adjointness in Krein Spaces; 1.3 Continuity of Separated Parts of the Spectrum; 1.3.1 Continuity of Resolvents; 1.3.2 Perturbation of Isolated Parts of the Spectrum; 1.3.3 Perturbation of Spectra of Self-Adjoint Operatorsin Hilbert Spaces; 1.3.4 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces
  • Chapter 2 Relatively Form-BoundedPerturbations in Krein Spaces2.1 Stability Theorems; 2.1.1 Accretive and Sectorial Operators; 2.1.2 Quadratic Forms and Associated Operators; 2.1.3 Relatively Form-Bounded and Relatively Form-Compact Operators; 2.2 Continuity of Separated Parts of the Spectrum; 2.2.1 Perturbation of Spectra of Self-Adjoint Operatorsin Hilbert Spaces; 2.2.2 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces; 2.3 Pseudo-Friedrichs Extensions; 2.3.1 Perturbation of Spectra of Self-Adjoint Operatorsin Krein Spaces; Chapter 3Examples; 3.1 Example 1; 3.2 Example 2
Control code
756192733
Dimensions
unknown
Extent
1 online resource
Form of item
online
Isbn
9783834817624
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-8348-8327-8
Specific material designation
remote
System control number
(OCoLC)756192733

Subject

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