The stability of matter in quantum mechanics:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2010
|
| Ausgabe: | 1. publ. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017739359&sequence=000003&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=017739359&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XV, 293 S. |
| ISBN: | 9780521191180 |
Internformat
MARC
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| 003 | DE-604 | ||
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| 245 | 1 | 0 | |a The stability of matter in quantum mechanics |c Elliott H. Lieb and Robert Seiringer |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XV, 293 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Matter |x Properties | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Structural stability | |
| 650 | 4 | |a Thomas-Fermi theory | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 PHY 022f 2013 A 4165 |
|---|---|
| DE-BY-TUM_katkey | 1937727 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040080043438 |
| _version_ | 1825257496711790592 |
| adam_text | Contents
Preface
xiii
1
Prologue
1
1.1
Introduction
1
1.2 Brief Outline
of the Book
5
2
Introduction to Elementary Quantum Mechanics and Stability
of the First Kind
8
2.1
A Brief Review of the Connection Between Classical and
Quantum Mechanics
8
2.1.1
Hamiltonian Formulation
10
2.1.2
Magnetic Fields
10
2.1.3
Relativistic Mechanics
12
2.1.4
Many-Body Systems
13
2.1.5
Introduction to Quantum Mechanics
14
2.1.6
Spin
18
2.1.7
Units
21
2.2
The Idea of Stability
24
2.2.1
Uncertainty Principles: Domination of the Potential
Energy by the Kinetic Energy
26
2.2.2
The Hydrogenic Atom
29
3
Many-Particle Systems and Stability of the Second Kind
31
3.1
Many-Body Wave Functions
31
3.1.1
The Space of Wave Functions
31
3.1.2
Spin
33
3.1.3
Bosons and
Fermions
(The
Pauli
Exclusion
Principle)
35
vu
Contents
3.1.4
Density
Matrices
38
3.1.5
Reduced Density Matrices
41
3.2
Many-Body Hamiltonians
50
3.2.1
Many-Body Hamiltonians and Stability: Models with
Static Nuclei
50
3.2.2
Many-Body Hamiltonians: Models without Static
Particles
54
3.2.3
Monotonicity
in the Nuclear Charges
57
3.2.4
Unrestricted Minimizers are Bosonic
58
Lieb-Thirring and Related Inequalities
62
4.1
LT Inequalities: Formulation
62
4.1.1
The Semiclassical Approximation
63
4.1.2
The LT Inequalities; Non-Relativistic Case
66
4.1.3
The LT Inequalities; Relativistic Case
68
4.2
Kinetic Energy Inequalities
70
4.3
The Birman-Schwinger Principle and LT Inequalities
75
4.3.1
The Birman-Schwinger Formulation of the
Schrödinger
Equation
75
4.3.2
Derivation of the LT Inequalities
77
4.3.3
Useful Corollaries
80
4.4
Diamagnetic Inequalities
82
4.5
Appendix: An Operator Trace Inequality
85
Electrostatic Inequalities
89
5.1
General Properties of the Coulomb Potential
89
5.2
Basic Electrostatic Inequality
92
5.3
Application: Baxter s Electrostatic Inequality
98
5.4
Refined Electrostatic Inequality
100
An Estimation of the Indirect Part of the Coulomb Energy
105
6.1
Introduction
105
6.2
Examples
107
6.3
Exchange Estimate
110
6.4
Smearing Out Charges
112
6.5
Proof of Theorem
6.1,
a First Bound
114
6.6
An Improved Bound
118
Contents ix
7
Stability of Non-Relativistic Matter
121
7.1
Proof of Stability of Matter
122
7.2
An Alternative Proof of Stability
125
7.3
Stability of Matter via Thomas-Fermi Theory
127
7.4
Other Routes to a Proof of Stability
129
7.4.1
Dyson-Lenard,
1967 130
7.4.2 Federbush, 1975 130
7.4.3
Some Later Work
130
7.5
Extensivity of Matter
131
7.6
Instability for Bosons
133
7.6.1
The N5/i Law
133
7.6.2
The/V7/5 Law
135
8
Stability of Relativistic Matter
139
8.1
Introduction
139
8.1.1
Heuristic Reason for a Bound on a Itself
140
8.2
The Relativistic One-Body Problem
141
8.3
A Localized Relativistic Kinetic Energy
145
8.4
A Simple Kinetic Energy Bound
146
8.5
Proof of Relativistic Stability
148
8.6
Alternative Proof of Relativistic Stability
154
8.7
Further Results on Relativistic Stability
156
8.8
Instability for Large a, Large
q
or Bosons
158
9
Magnetic Fields and the
Pauli
Operator
164
9.1
Introduction
164
9.2
The
Pauli
Operator and the Magnetic Field Energy
165
9.3
Zero-Modes of the
Pauli
Operator
166
9.4
A Hydrogenic Atom in a Magnetic Field
168
9.5
The Many-Body Problem with a Magnetic Field
171
9.6
Appendix: BKS Inequalities
178
10
The Dirac Operator and the Brown-Ravenhall Model
181
10.1
The Dirac Operator
181
10.1.1
Gauge
Invariance
184
10.2
Three Alternative Hubert Spaces
185
10.2.1
The Brown-Ravenhall Model
186
Contents
10.2.2
A Modified Brown-Ravenhall Model
187
10.2.3
The Furry Picture
188
10.3
The One-Particle Problem
189
10.3.1
The Lonely Dirac Particle in a Magnetic Field
189
10.3.2
The Hydrogenic Atom in a Magnetic Field
190
10.4
Stability of the Modified Brown-Ravenhall Model
193
10.5
Instability of the Original Brown-Ravenhall Model
196
10.6
The Non-Relativistic Limit and the
Pauli
Operator
198
11
Quantized Electromagnetic Fields and Stability of Matter
200
11.1
Review of Classical Electrodynamics and its Quantization
200
11.1.1
Maxwell s Equations
200
11.1.2
Lagrangian and Hamiltonian of the Electromagnetic
Field
204
11.1.3
Quantization of the Electromagnetic Field
207
11.2 Pauli
Operator with Quantized Electromagnetic Field
210
11.3
Dirac Operator with Quantized Electromagnetic Field
217
12
The Ionization Problem, and the Dependence of the Energy on
N
and
M
Separately
221
12.1
Introduction
221
12.2
Bound on the Maximum Ionization
222
12.3
How Many Electrons Can an Atom or Molecule Bind?
228
13
Gravitational Stability of White Dwarfs and Neutron Stars
233
13.1
Introduction and Astrophysical Background
233
13.2
Stability and Instability Bounds
235
13.3
A More Complete Picture
240
13.3.1
Relativistic Gravitating
Fermions
240
13.3.2
Relativistic Gravitating Bosons
242
13.3.3
Inclusion of Coulomb Forces
243
14
The Thermodynamic Limit for Coulomb Systems
247
14.1
Introduction
247
14.2
Thermodynamic Limit of the Ground State Energy
249
14.3
Introduction to Quantum Statistical Mechanics and the
Thermodynamic Limit
252
Contents xi
14.4
A
Brief
Discussion of Classical Statistical Mechanics
258
14.5
The Cheese Theorem
260
14.6
Proof of Theorem
14.2 263
14.6.1
Proof for Special Sequences
263
14.6.2
Proof for General Domains
268
14.6.3
Convexity
270
14.6.4
General Sequences of Particle Numbers
271
14.7
The Jellium Model
271
List of Symbols
276
Bibliography
279
Index
290
Research
into the stability of matter has been one of the most
successful chapters in mathematical physics, and is a prime example of
how modern mathematics can be applied to problems in physics.
A unique account of the subject, this book provides a complete, self-
contained description of research on the stability of matter problem. It
introduces the necessary quantum mechanics to mathematicians, and
aspects of functional analysis to physicists. The topics covered include
electrodynamics of classical and quantized fields, Lieb-Thirring and
other inequalities in spectral theory, inequalities in electrostatics,
stability of large Coulomb systems, gravitational stability of stars, basics
of equilibrium statistical mechanics, and the existence of the
thermodynamic limit.
The book is an up-to-date account for researchers, and its
pedagogical style makes it suitable for advanced undergraduate and
graduate courses in mathematical physics.
Elliott H.
lieb
is a Professor of Mathematics and Higgins
Professor of Physics at Princeton University. He has been a leader of
research in mathematical physics for many decades, and his
achievements have earned him numerous prizes and awards.
Robert SEiRiNGERisan Assistant Professor of Physics at
Princeton University, where his research is centered largely on the
quantum-mechanical many-body problem.
|
| any_adam_object | 1 |
| author | Lieb, Elliott H. 1932- Seiringer, Robert |
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| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035685166 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:40:37Z |
| institution | BVB |
| isbn | 9780521191180 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017739359 |
| oclc_num | 429816927 |
| open_access_boolean | |
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| owner_facet | DE-19 DE-BY-UBM DE-703 DE-355 DE-BY-UBR DE-11 DE-91G DE-BY-TUM |
| physical | XV, 293 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Lieb, Elliott H. 1932- Seiringer, Robert The stability of matter in quantum mechanics Quantentheorie Matter Properties Quantum theory Structural stability Thomas-Fermi theory Thomas-Fermi-Modell (DE-588)4185321-0 gnd Quantenmechanik (DE-588)4047989-4 gnd Stabilität (DE-588)4056693-6 gnd Materie (DE-588)4037940-1 gnd |
| subject_GND | (DE-588)4185321-0 (DE-588)4047989-4 (DE-588)4056693-6 (DE-588)4037940-1 |
| title | The stability of matter in quantum mechanics |
| title_auth | The stability of matter in quantum mechanics |
| title_exact_search | The stability of matter in quantum mechanics |
| title_full | The stability of matter in quantum mechanics Elliott H. Lieb and Robert Seiringer |
| title_fullStr | The stability of matter in quantum mechanics Elliott H. Lieb and Robert Seiringer |
| title_full_unstemmed | The stability of matter in quantum mechanics Elliott H. Lieb and Robert Seiringer |
| title_short | The stability of matter in quantum mechanics |
| title_sort | the stability of matter in quantum mechanics |
| topic | Quantentheorie Matter Properties Quantum theory Structural stability Thomas-Fermi theory Thomas-Fermi-Modell (DE-588)4185321-0 gnd Quantenmechanik (DE-588)4047989-4 gnd Stabilität (DE-588)4056693-6 gnd Materie (DE-588)4037940-1 gnd |
| topic_facet | Quantentheorie Matter Properties Quantum theory Structural stability Thomas-Fermi theory Thomas-Fermi-Modell Quantenmechanik Stabilität Materie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017739359&sequence=000003&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=017739359&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT liebelliotth thestabilityofmatterinquantummechanics AT seiringerrobert thestabilityofmatterinquantummechanics |
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