Bohmian mechanics: the physics and mathematics of quantum theory
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 393 S. Ill., graph. Darst. |
| ISBN: | 9783540893431 |
Internformat
MARC
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| 240 | 1 | 0 | |a Bohmsche Mechanik als Grundlage der Quantenmechanik |
| 245 | 1 | 0 | |a Bohmian mechanics |b the physics and mathematics of quantum theory |c Detlef Dürr ; Stefan Teufel |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XII, 393 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Bohmsche Quantenmechanik | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory |x Mathematics | |
| 650 | 0 | 7 | |a Bohmsche Quantenmechanik |0 (DE-588)4414469-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Bohmsche Quantenmechanik |0 (DE-588)4414469-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Teufel, Stefan |d 1970- |e Verfasser |0 (DE-588)121295303 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-89344-8 |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017682101 | ||
Datensatz im Suchindex
| _version_ | 1804139300933074944 |
|---|---|
| adam_text | Titel: Bohmian mechanics
Autor: Dürr, Detlef
Jahr: 2009
Contents
1 Introduction................................................... I
1.1 Ontology: What There Is.................................... 1
1.1.1 Extracts............................................ I
1.1.2 In Brief: The Problem of Quantum Mechanics............ 4
1.1.3 In Brief: Bohmian Mechanics.......................... 6
1.2 Determinism and Realism ................................... 9
References..................................................... 10
2 Classical Physics............................................... 11
2.1 Newtonian Mechanics....................................... 12
2.2 Hamiltonian Mechanics..................................... 13
2.3 Hamilton-Jacobi Formulation................................ 24
2.4 Fields and Particles: Electromagnetism ........................ 26
2.5 No fields, Only Particles: Electromagnetism.................... 34
2.6 On the Symplectic Structure of the Phase Space................. 38
References..................................................... 42
3 Symmetry..................................................... 43
4 Chance ....................................................... 49
4.1 Typicality................................................. 51
4.1.1 Typical Behavior. The Law of Large Numbers............ 54
4.1.2 Statistical Hypothesis and Its Justification................ 63
4.1.3 Typicality in Subsystems:
Microcanonical and Canonical Ensembles ............... 66
4.2 Irreversibility.............................................. 80
4.2.1 Typicality Within Atypicality.......................... 81
4.2.2 Our Atypical Universe................................ 89
4.2.3 Ergodicity and Mixing................................ 90
4.3 Probability Theory ......................................... 96
4.3.1 Lebesgue Measure and Coarse-Graining................. 96
x Contents
4.3.2 The Law of Large Numbers ...........................102
References.....................................................107
5 Brownian motion ..............................................109
5.1 Einstein s Argument........................................110
5.2 On Smoluchowski s Microscopic Derivation....................114
5.3 Path Integration............................................118
References.....................................................119
6 The Beginning of Quantum Theory ..............................121
References.....................................................127
7 Schrodinger s Equation.........................................129
7.1 The Equation..............................................129
7.2 What Physics Must Not Be ..................................135
7.3 Interpretation, Incompleteness, and p = ff 2 ...................139
References.....................................................143
8 Bohmian Mechanics............................................145
8.1 Derivation of Bohmian Mechanics............................147
8.2 Bohmian Mechanics and Typicality ...........................151
8.3 Electron Trajectories........................................153
8.4 Spin......................................................158
8.5 A Topological View of Indistinguishable Particles...............166
References.....................................................171
9 The Macroscopic World ........................................173
9.1 Pointer Positions...........................................173
9.2 Effective Collapse..........................................179
9.3 Centered Wave packets......................................183
9.4 The Classical Limit of Bohmian Mechanics.....................186
9.5 Some Further Observations..................................191
9.5.1 Dirac Formalism, Density Matrix,
Reduced Density Matrix, and Decoherence...............191
9.5.2 Poincare Recurrence .................................198
References.....................................................200
10 Nonlocality....................................................201
10.1 Singlet State and Probabilities for Anti-Correlations .............205
10.2 Faster Than Light Signals?...................................208
References.....................................................209
11 The Wave Function and Quantum Equilibrium....................211
11.1 Measure of Typicality.......................................211
11.2 Conditional Wave Function..................................213
11.3 Effective Wave function.....................................216
Contents xi
11.4 Typical Empirical Distributions...............................218
11.5 Misunderstandings .........................................223
11.6 Quantum Nonequilibrium....................................224
References.....................................................225
12 From Physics to Mathematics ...................................227
12.1 Observables. An Unhelpful Notion............................227
12.2 Who Is Afraid of PVMs and POVMs?.........................233
12.2.1 The Theory Decides What Is Measurable................241
12.2.2 Joint Probabilities....................................242
12.2.3 Naive Realism about Operators ........................244
12.3 Schrodinger s Equation Revisited.............................245
12.4 What Comes Next?.........................................248
References.....................................................249
13 Hilbert Space..................................................251
13.1 The Hilbert Space L2 .......................................253
13.1.1 The Coordinate Space f..............................255
13.1.2 Fourier Transformation on I?..........................258
13.2 Bilinear Forms and Bounded Linear Operators..................268
13.3 Tensor Product Spaces......................................271
References.....................................................278
14 The Schrodinger Operator......................................279
14.1 Unitary Groups and Their Generators..........................279
14.2 Self-Adjoint Operators......................................284
14.3 The Atomistic Schrodinger Operator..........................294
References.....................................................298
15 Measures and Operators........................................299
15.1 Examples of PVMs and Their Operators.......................303
15.1.1 Heisenberg Operators.................................305
15.1.2 Asymptotic Velocity and the Momentum Operator........306
15.2 The Spectral Theorem.......................................311
15.2.1 The Dirac Formalism.................................311
15.2.2 Mathematics of the Spectral Theorem...................313
15.2.3 Spectral Representations..............................322
15.2.4 Unbounded Operators................................324
15.2.5 Unitary Groups......................................332
15.2.6 Ho = -A/2.........................................333
15.2.7 The Spectrum.......................................341
References.....................................................344
xii Contents
16 Bohmian Mechanics on Scattering Theory........................345
16.1 Exit Statistics..............................................346
16.2 Asymptotic Exits...........................................353
16.3 Scattering Theory and Exit Distribution........................356
16.4 More on Abstract Scattering Theory...........................358
16.5 Generalized Eigenfunctions..................................361
16.6 Towards the Scattering Cross-Section..........................368
16.7 The Scattering Cross-Section.................................369
16.7.1 Born s Formula......................................370
16.7.2 Time-Dependent Scattering............................372
References.....................................................378
17 Epilogue......................................................379
References.....................................................380
Bibliography.......................................................381
Index.............................................................387
|
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| dewey-ones | 530 - Physics |
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| id | DE-604.BV035627075 |
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| indexdate | 2024-07-09T21:41:54Z |
| institution | BVB |
| isbn | 9783540893431 |
| language | English |
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| physical | XII, 393 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
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| publisher | Springer |
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| spelling | Dürr, Detlef 1951-2021 Verfasser (DE-588)10956863X aut Bohmsche Mechanik als Grundlage der Quantenmechanik Bohmian mechanics the physics and mathematics of quantum theory Detlef Dürr ; Stefan Teufel Berlin [u.a.] Springer 2009 XII, 393 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Bohmsche Quantenmechanik Mathematik Quantentheorie Quantum theory Mathematics Bohmsche Quantenmechanik (DE-588)4414469-6 gnd rswk-swf Bohmsche Quantenmechanik (DE-588)4414469-6 s DE-604 Teufel, Stefan 1970- Verfasser (DE-588)121295303 aut Erscheint auch als Online-Ausgabe 978-3-540-89344-8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017682101&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dürr, Detlef 1951-2021 Teufel, Stefan 1970- Bohmian mechanics the physics and mathematics of quantum theory Bohmsche Quantenmechanik Mathematik Quantentheorie Quantum theory Mathematics Bohmsche Quantenmechanik (DE-588)4414469-6 gnd |
| subject_GND | (DE-588)4414469-6 |
| title | Bohmian mechanics the physics and mathematics of quantum theory |
| title_alt | Bohmsche Mechanik als Grundlage der Quantenmechanik |
| title_auth | Bohmian mechanics the physics and mathematics of quantum theory |
| title_exact_search | Bohmian mechanics the physics and mathematics of quantum theory |
| title_full | Bohmian mechanics the physics and mathematics of quantum theory Detlef Dürr ; Stefan Teufel |
| title_fullStr | Bohmian mechanics the physics and mathematics of quantum theory Detlef Dürr ; Stefan Teufel |
| title_full_unstemmed | Bohmian mechanics the physics and mathematics of quantum theory Detlef Dürr ; Stefan Teufel |
| title_short | Bohmian mechanics |
| title_sort | bohmian mechanics the physics and mathematics of quantum theory |
| title_sub | the physics and mathematics of quantum theory |
| topic | Bohmsche Quantenmechanik Mathematik Quantentheorie Quantum theory Mathematics Bohmsche Quantenmechanik (DE-588)4414469-6 gnd |
| topic_facet | Bohmsche Quantenmechanik Mathematik Quantentheorie Quantum theory Mathematics |
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