Hilbert space operators in quantum physics:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[New York, NY]
Springer
2008
|
| Edition: | 2. ed. |
| Series: | Theoretical and Mathematical Physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 664 S. |
| ISBN: | 9781402088698 |
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MARC
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| 100 | 1 | |a Blank, Jiří |d 1939-1990 |e Verfasser |0 (DE-588)142642738 |4 aut | |
| 245 | 1 | 0 | |a Hilbert space operators in quantum physics |c Jirí Blank ; Pavel Exner ; Miloslav Havlícek |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a [New York, NY] |b Springer |c 2008 | |
| 300 | |a XVII, 664 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Theoretical and Mathematical Physics | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Hilbert space | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Quantum theory | |
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| 700 | 1 | |a Exner, Pavel |d 1946- |e Verfasser |0 (DE-588)134284410 |4 aut | |
| 700 | 1 | |a Havlíček, Miroslav |e Verfasser |0 (DE-588)172129184 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-402-08870-4 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017151690 | ||
Record in the Search Index
| _version_ | 1804138666554032128 |
|---|---|
| adam_text | Contents
Preface
to the second edition
vii
Preface
ix
1
Some notions from functional analysis
1
1.1
Vector and normed spaces
........................ 1
1.2
Metric and topological spaces
...................... 5
1.3
Compactness
............................... 10
1.4
Topological vector spaces
......................... 13
1.5
Banach spaces and operators on them
.................. 15
1.6
The principle of uniform boundedness
.................. 23
1.7
Spectra of closed linear operators
.................... 25
Notes to Chapter
1............................... 29
Problems
.................................... 32
2
Hubert spaces
41
2.1
The geometry of Hilbert spaces
..................... 41
2.2
Examples
................................. 45
2.3
Direct sums of Hilbert spaces
...................... 50
2.4
Tensor products
.............................. 54
Notes to Chapter
2............................... 56
Problems
.................................... 59
3
Bounded operators
63
3.1
Basic notions
............................... 63
3.2
Hermitean operators
........................... 67
3.3
Unitary and isometric operators
..................... 72
3.4
Spectra of bounded normal operators
.................. 74
3.5
Compact operators
............................ 77
3.6
Hilbert-Schmidt and trace-class operators
............... 81
Notes to Chapter
3............................... 87
Problems
.................................... 88
xiii
r
Contents
Unbounded operators
93
4.1
The adjoint
................................
93
4.2
Closed operators
............................. 95
4.3
Normal operators. Self-adjointness
...................100
4.4
Reducibility. Unitary equivalence
....................105
4.5
Tensor products
..............................108
4.6
Quadratic forms
..............................
HO
4.7
Self-adjoint extensions
..........................117
4.8
Ordinary differential operators
......................126
4.9
Self-adjoint extensions of differential operators
.............133
Notes to Chapter
4...............................139
Problems
....................................142
Spectral theory
151
5.1
Projection-valued measures
.......................151
5.2
Functional calculus
............................156
5.3
The spectral theorem
...........................165
5.4
Spectra of self-adjoint operators
.....................171
5.5
Functions of self-adjoint operators
....................176
5.6
Analytic vectors
..............................183
5.7
Tensor products
..............................185
5.8
Spectral representation
..........................187
5.9
Groups of unitary operators
.......................191
Notes to Chapter
5...............................195
Problems
....................................197
Operator sets and algebras
205
6.1
C* -algebras
................................205
6.2
GNS construction
.............................208
6.3
W-algebras
................................213
6.4
Normal states on W-algebras
......................221
6.5
Commutative symmetric operator sets
.................227
6.6
Complete sets of commuting operators
.................232
6.7
Irreducibility. Functions of non-commuting operators
.........235
6.8
Algebras of unbounded operators
....................239
Notes to Chapter
6...............................241
Problems
....................................246
States and
observables
251
7.1
Basic postulates
..............................251
7.2
Simple examples
.............................259
7.3
Mixed states
................................264
7.4
Supersełection
rules
............................268
7.5
Compatibility
...............................273
Contents xv
7.6
The algebraic approach
..........................282
Notes to Chapter
7...............................285
Problems
....................................289
8
Position and momentum
293
8.1
Uncertainty relations
...........................293
8.2
The canonical commutation relations
..................299
8.3
The classical limit and quantization
...................306
Notes to Chapter
8...............................310
Problems
....................................313
9
Time evolution
317
9.1
The fundamental postulate
........................317
9.2
Pictures of motion
............................323
9.3
Two examples
...............................325
9.4
The Feynman integral
..........................330
9.5
Nonconservative
systems
.........................334
9.6
Unstable systems
.............................340
Notes to Chapter
9...............................348
Problems
....................................354
10
Symmetries of quantum systems
357
10.1
Basic notions
...............................357
10.2
Some examples
..............................362
10.3
General space-time transformations
...................370
Notes to Chapter
10..............................373
Problems
....................................375
11
Composite systems
379
11.1
States and
observables
..........................379
11.2
Reduced states
..............................383
11.3
Time evolution
..............................388
11.4
Identical particles
.............................389
11.5
Separation of variables. Symmetries
...................392
Notes to Chapter
11 ..............................398
Problems
....................................400
12
The second quantization
403
12.1
Fock spaces
................................403
12.2
Creation and annihilation operators
...................408
12.3
Systems of noninteracting particles
...................413
Notes to Chapter
12..............................420
Problems
....................................423
xvj
Contents
13
Axiomatization
of quantum theory
425
13.1
Lattices of propositions
..........................425
13.2
States on proposition systems
......................430
13.3
Axioms for quantum field theory
....................434
Notes to Chapter
13..............................438
Problems
....................................441
14 Schrödinger
operators
443
14.1
Self-adjointness
..............................443
14.2
The minimax principle. Analytic perturbations
.............448
14.3
The discrete spectrum
..........................454
14.4
The essential spectrum
..........................462
14.5
Constrained motion
............................471
14.6
Point and contact interactions
......................474
Notes to Chapter
14..............................479
Problems
....................................486
15
Scattering theory
491
15.1
Basic notions
...............................491
15.2
Existence of wave operators
.......................498
15.3
Potential scattering
............................506
15.4
A model of two-channel scattering
...................510
Notes to Chapter
15..............................521
Problems
....................................524
16
Quantum waveguides
527
16.1
Geometric effects in Dirichlet stripes
..................527
16.2
Point perturbations
............................532
16.3
Curved quantum layers
..........................539
16.4
Weak coupling
...............................547
Notes to Chapter
16..............................552
Problems
....................................555
17
Quantum graphs
561
17.1
Admissible Hamiltonians
.........................561
17.2
Meaning of the vertex coupling
.....................566
17.3
Spectral and scattering properties
....................570
17.4
Generalized graphs
............................579
17.5
Leaky graphs
...............................580
Notes to Chapter
17..............................587
Problems
....................................590
Contents xvii
A Measure and integration
595
A.I Sets, mappings, relations
.........................595
A.2 Measures and measurable functions
...................598
A.3 Integration
.................................601
A.4 Complex measures
............................605
A.5 The Bochner integral
...........................607
В
Some algebraic notions
609
B.I Involutive algebras
............................609
B.2 Banach algebras
..............................612
B.3 Lie algebras and Lie groups
.......................614
References
617
List of symbols
647
Index
651
|
| any_adam_object | 1 |
| author | Blank, Jiří 1939-1990 Exner, Pavel 1946- Havlíček, Miroslav |
| author_GND | (DE-588)142642738 (DE-588)134284410 (DE-588)172129184 |
| author_facet | Blank, Jiří 1939-1990 Exner, Pavel 1946- Havlíček, Miroslav |
| author_role | aut aut aut |
| author_sort | Blank, Jiří 1939-1990 |
| author_variant | j b jb p e pe m h mh |
| building | Verbundindex |
| bvnumber | BV035347488 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.17.H55 |
| callnumber-search | QC174.17.H55 |
| callnumber-sort | QC 3174.17 H55 |
| callnumber-subject | QC - Physics |
| classification_rvk | SK 600 SK 620 SK 950 UK 1200 UK 3000 |
| classification_tum | PHY 020f MAT 463f |
| ctrlnum | (OCoLC)277069452 (DE-599)DNB990587738 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik Geographie |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV035347488 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:31:49Z |
| institution | BVB |
| isbn | 9781402088698 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017151690 |
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| physical | XVII, 664 S. |
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| series2 | Theoretical and Mathematical Physics |
| spelling | Blank, Jiří 1939-1990 Verfasser (DE-588)142642738 aut Hilbert space operators in quantum physics Jirí Blank ; Pavel Exner ; Miloslav Havlícek 2. ed. [New York, NY] Springer 2008 XVII, 664 S. txt rdacontent n rdamedia nc rdacarrier Theoretical and Mathematical Physics Mathematische Physik Quantentheorie Hilbert space Mathematical physics Quantum theory Quantentheorie (DE-588)4047992-4 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Quantentheorie (DE-588)4047992-4 s DE-604 Exner, Pavel 1946- Verfasser (DE-588)134284410 aut Havlíček, Miroslav Verfasser (DE-588)172129184 aut Erscheint auch als Online-Ausgabe 978-1-402-08870-4 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017151690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blank, Jiří 1939-1990 Exner, Pavel 1946- Havlíček, Miroslav Hilbert space operators in quantum physics Mathematische Physik Quantentheorie Hilbert space Mathematical physics Quantum theory Quantentheorie (DE-588)4047992-4 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4159850-7 |
| title | Hilbert space operators in quantum physics |
| title_auth | Hilbert space operators in quantum physics |
| title_exact_search | Hilbert space operators in quantum physics |
| title_full | Hilbert space operators in quantum physics Jirí Blank ; Pavel Exner ; Miloslav Havlícek |
| title_fullStr | Hilbert space operators in quantum physics Jirí Blank ; Pavel Exner ; Miloslav Havlícek |
| title_full_unstemmed | Hilbert space operators in quantum physics Jirí Blank ; Pavel Exner ; Miloslav Havlícek |
| title_short | Hilbert space operators in quantum physics |
| title_sort | hilbert space operators in quantum physics |
| topic | Mathematische Physik Quantentheorie Hilbert space Mathematical physics Quantum theory Quantentheorie (DE-588)4047992-4 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Mathematische Physik Quantentheorie Hilbert space Mathematical physics Quantum theory Hilbert-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017151690&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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