Determining spectra in quantum theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2005
|
| Series: | Progress in mathematical physics
44 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | X, 219 S. |
| ISBN: | 0817643664 9780817643669 |
Staff View
MARC
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| 100 | 1 | |a Demuth, Michael |d 1946- |e Verfasser |0 (DE-588)130367478 |4 aut | |
| 245 | 1 | 0 | |a Determining spectra in quantum theory |c Michael Demuth ; M. Krishna |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2005 | |
| 300 | |a X, 219 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematical physics |v 44 | |
| 650 | 4 | |a Operator theory | |
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| 650 | 4 | |a Scattering (Mathematics) | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
v
1
Measures and Transforms
.................................. 1
1.1
Measures
............................................... 1
1.2
Fourier Transform
....................................... 5
1.3
The Wavelet Transform
.................................. 7
1.4
Borei
Transform
......................................... 16
1.5
Gesztesy-Krein-Simon
ξ
Function
......................... 24
1.6
Notes
.................................................. 25
2
Selfadjointness and Spectrum
.............................. 29
2.1
Selfadjointness
........................................... 29
2.1.1
Linear Operators and Their Inverses
................. 29
2.1.2
Closed Operators
.................................. 30
2.1.3
Adjoint and Selfadjoint Operators
................... 32
2.1.4
Sums of Linear Operators
.......................... 34
2.1.5
Sesquilinear Forms
................................ 35
2.2
Spectrum and Resolvent Sets
............................. 37
2.3
Spectral Theorem
....................................... 40
2.4
Spectral Measures and Spectrum
.......................... 43
2.5
Spectral Theorem in the Hahn-Hellinger Form
.............. 45
2.6
Components of the Spectrum
............................. 49
2.7
Characterization of the States in Spectral Subspaces
......... 53
2.8
Notes
.................................................. 56
3
Criteria for Identifying the Spectrum
...................... 59
3.1
Borei
Transform
........................................ 59
3.2
Fourier Transform
....................................... 68
3.3
Wavelet Transform
...................................... 69
3.4
Eigenfunctions
.......................................... 70
3.5
Commutators
.......................................... 72
χ
Contents
3.6
Criteria
Using Scattering Theory
.......................... 80
3.6.1
Wave Operators
................................... 81
3.6.2
Stability of the Absolutely Continuous Spectra
........ 95
3.7
Notes
..................................................104
4
Operators of Interest
......................................
Ill
4.1
Unperturbed Operators
..................................
Ill
4.1.1
Laplacians
........................................112
4.1.2
Unperturbed Semigroups and Their Kernels
..........119
4.1.3
Associated Processes
...............................120
4.1.4
Regular Dirichlet Forms, Capacities and Equilibrium
Potentials
........................................121
4.2
Perturbed Operators
.....................................125
4.2.1
Deterministic Potentials
............................125
4.2.2
Random Potentials
................................133
4.2.3
Singular Perturbations
.............................135
4.3
Notes
..................................................142
5
Applications
...............................................153
5.1
Borei
Transforms
........................................153
5.1.1
Kotani Theory
....................................153
5.1.2
Aizenman-Molchanov Method
......................160
5.1.3
Bethe Lattice
.....................................172
5.1.4
Jaksić-Last
Theorem
..............................181
5.2
Scattering
..............................................183
5.2.1
Decaying Random Potentials
........................183
5.2.2
Obstacles and Potentials
...........................187
5.3
Notes
..................................................196
References
.....................................................203
Index
..........................................................215
Michael Demuth and
M. Krishna
Determining Spectra in
Quantum
Theory
The spectral theory of Schrodinger operators, in particular those with
random potentials, continues to be a very active field of research. This
work focuses on various known criteria in the spectral theory ol sell adjoint
operators in order to identify the spectrum and its components
à la
I.ebesgue decomposition.
Key features and topics:
•
Well-developed exposition of criteria that are especially useful in
determining the spectra of deterministic and random Schrodinger
operators occurring in quantum theory
•
Systematically uses measures and their transforms
(
Fourier.
Borei,
wavelet
)
to present a unifying theme
•
Establishes criteria for identifying the spectrum
•
Examines a series of applications to show point spectrum and continuous
spectrum in some models of random operators
•
Presents a series of spectral-theoretic results for the perturbed operator»
introduced in the earlier chapters with examples of localization
and delocalization in the theory of disordered systems
•
Presents modern criteria (using wavelet transform, eigenfunction decav
ι
that could be used to do spectral theory
•
Unique work in book form combining the presentation of the
deterministic and random cases, which will serve as a platform for
further research activities
This concise unified presentation is aimed at graduate students and
researchers working in the spectral theory of Schrodinger operators with
either fixed or random potentials in particular. However, given the large
gap that this book fills in the literature, it will serve a wider audience of
mathematical phvsicists in its contribution to works in spectral theory.
|
| any_adam_object | 1 |
| author | Demuth, Michael 1946- Krishna, Maddaly |
| author_GND | (DE-588)130367478 |
| author_facet | Demuth, Michael 1946- Krishna, Maddaly |
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| dewey-full | 515/.7222 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Physik Mathematik |
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| spelling | Demuth, Michael 1946- Verfasser (DE-588)130367478 aut Determining spectra in quantum theory Michael Demuth ; M. Krishna Boston [u.a.] Birkhäuser 2005 X, 219 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematical physics 44 Operator theory Potential theory (Mathematics) Scattering (Mathematics) Spectral theory (Mathematics) Selbstadjungierter Operator (DE-588)4180810-1 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Hamilton-Operator (DE-588)4072278-8 s Selbstadjungierter Operator (DE-588)4180810-1 s Spektraltheorie (DE-588)4116561-5 s DE-604 Krishna, Maddaly Verfasser aut Progress in mathematical physics 44 (DE-604)BV013823265 44 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Demuth, Michael 1946- Krishna, Maddaly Determining spectra in quantum theory Progress in mathematical physics Operator theory Potential theory (Mathematics) Scattering (Mathematics) Spectral theory (Mathematics) Selbstadjungierter Operator (DE-588)4180810-1 gnd Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4180810-1 (DE-588)4072278-8 (DE-588)4116561-5 |
| title | Determining spectra in quantum theory |
| title_auth | Determining spectra in quantum theory |
| title_exact_search | Determining spectra in quantum theory |
| title_full | Determining spectra in quantum theory Michael Demuth ; M. Krishna |
| title_fullStr | Determining spectra in quantum theory Michael Demuth ; M. Krishna |
| title_full_unstemmed | Determining spectra in quantum theory Michael Demuth ; M. Krishna |
| title_short | Determining spectra in quantum theory |
| title_sort | determining spectra in quantum theory |
| topic | Operator theory Potential theory (Mathematics) Scattering (Mathematics) Spectral theory (Mathematics) Selbstadjungierter Operator (DE-588)4180810-1 gnd Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Operator theory Potential theory (Mathematics) Scattering (Mathematics) Spectral theory (Mathematics) Selbstadjungierter Operator Hamilton-Operator Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013354431&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013823265 |
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