Lectures in quantum mechanics: a two-term course
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| Main Author: | |
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| Format: | Book |
| Language: | English |
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Cham
Springer
[2016]
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| Series: | UNITEXT for physics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 354 Seiten Diagramme |
| ISBN: | 3319226312 9783319226316 |
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Record in the Search Index
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| adam_text | Titel: Lectures in quantum mechanics
Autor: Picasso, Luigi E
Jahr: 2016
Contents
1 The Crisis of Classical Physics
1.1 Atomic Models...............................................1
1.2 The Problems of Atomic Size and Radiative Collapse......... 5
1.3 Difficulties Related with Heat Capacities .................... 7
1.4 Photoelectric Effect ......................................... 12
2 From Einstein to de Broglie
2.1 Photons .................................................... 15
2.2 Compton Effect............................................. 17
2.3 General Features of Spectra. Bohr Hypotheses .............. 18
2.4 Hydrogen Energy Levels According to Bohr ................. 21
2.5 Energy Levels for an Oscillator and for a Particle
in a Segment ............................................... 25
2.6 Einstein and Debye Theories for the Heat Capacities
of Solids .................................................... 27
2.7 Heat Capacities of Gases ....................................34
2.8 Wave-like Behaviour of Particles: the Bragg
and Davisson-Germer Experiments......................... 38
3 Introduction to the Postulates of Quantum Mechanics
3.1 Introduction ................................................ 43
3.2 The Mach-Zehnder Interferometer .......................... 44
3.3 One Photon Interference Experiments.......................45
3.4 Description of the Polarization States of a Photon...........49
3.5 Discussion of Experiments with Polaroid Sheets ............. 52
3.6 Compatible and Incompatible Measurements:
Heisenberg Uncertainty Relation ............................ 57
4 The Postulates of Quantum Mechanics
4.1 The Superposition Principle ................................ 61
4.2 Observables.................................................63
4.3 Transition Probabilities ..................................... 66
4.4 Consequences and von Neumann Postulate..................68
VIII
Contents
4.5 Operators Associated with Observables ..........................................72
4.6 Properties of the Operators Associated with Observables — 73
4.7 Digression on Dirac Notation ..............................................................76
4.8 Mean Values................................................78
4.9 Pure States and Statistical Mixtures ................................................80
4.10 Compatible Observables ........................................................................84
4.11 Uncertainty Relations.......................................89
4.12 Quantization Postulate ..........................................................................90
5 The Harmonic Oscillator
5.1 Positivity of the Eigenvalues of Energy......................95
5.2 The Energy Levels of the Harmonic Oscillator...............97
6 Representation Theory
6.1 Representations ........................................... 101
6.2 Heisenberg Representation for the Harmonic Oscillator.....104
6.3 Unitary Transformations...................................106
6.4 The Schrodinger Representation: Preliminary
Considerations.............................................109
6.5 The Schrodinger Representation ........................... 112
6.6 Physical Interpretation of Schrodinger and Momentum
Representations ........................................... 119
6.7 The Improper Eigenvectors of qi and p., .................... 121
6.8 The Relationship between Coordinate and Momentum
Representations ........................................... 124
6.9 The q and p as Observables ................................ 128
7 Schrodinger Equation for One-Dimensional Systems
7.1 The Hamiltonian for the Free Particle......................133
7.2 Degeneracy Theorem. Spatial Inversions ................... 135
7.3 General Features of the Solutions of Schrodinger Equation
in the One-Dimensional Case .............................. 139
7.4 Solutions of Schrodinger Equation: Discrete Eigenvalues____141
7.5 Solutions of Schrodinger Equation: Continuous Eigenvalues 145
8 One-Dimensional Systems
8.1 The One-Dimensional Harmonic Oscillator
in the Schrodinger Representation ......................... 149
8.2 Potential Well ............................................. 152
8.3 Tunnel Effect.............................................. 157
9 Time-Evolution
9.1 Time-Evolution in the Schrodinger Picture.................161
9.2 Time-Evolution in the Heisenberg Picture..................168
9.3 The Classical Limit of Quantum Mechanics ................ 170
10 Angular Momentum
10.1 Angular Momentum: Commutation Rules.................. 175
10.2 Angular Momentum: Eigenvalues .......................... 178
Contents
IX
10.3 Rotation Operators ........................................ 182
10.4 Orbital Angular Momentum ............................... 183
11 Particle in a Central Force Field
11.1 The Schrodinger Equation in a Central Force Field.........187
11.2 Two-Particle Systems: Separation of Variables ..........................190
11.3 Energy Levels of Hydrogen-like Atoms ..........................................194
11.4 The Three-Dimensional Isotropic Harmonic Oscillator......199
12 Perturbations to Energy Levels
12.1 Perturbation Theory: Heuristic Approach .................. 203
12.2 The Stark Effect in the Hydrogen Atom ................... 206
12.3 First-Order Perturbation Theory: Formal Treatment ....... 212
12.4 Second-Order Perturbation Theory and Quasi-Degenerate
Levels ..................................................... 214
13 Electromagnetic Transitions
13.1 Introduction............................................... 219
13.2 Perturbation Theory for Time-Evolution................... 220
13.3 Semiclassical Theory of Radiation ......................... 223
13.4 Spontaneous Emission ..................................... 227
13.5 Electric-Dipole Transitions.................................230
13.6 Selection Rules I .......................................... 232
13.7 Atom in Magnetic Field: the Normal Zeeman Effect ........236
13.8 Polarization and Angular Distribution of Emitted Radiation 241
13.9 The Lifetime of the n = 2 Energy Level of Hydrogen Atom . 243
14 Introduction to Atomic Physics
14.1 The Central-Field Approximation..........................247
14.2 The Variational Method ................................... 251
14.3 The Lowest Energy Level of Helium ....................... 253
14.4 The Alkali Atoms..........................................256
14.5 Quantum Treatment of the Alkali Atoms .................. 260
15 Composite Systems. Pauli Principle
15.1 The Hilbert Space for a System with Many Particles:
Tensor Product of Hilbert Spaces .......................... 267
15.2 The Spin of the Electron...................................269
15.3 Composition of Angular Momenta ......................... 272
15.4 Pauli Exclusion Principle .................................. 277
16 Many-Electron Atoms
16.1 The Energy Levels of the Helium Atom .................... 283
16.2 Classification of the Energy Levels of Atoms ............... 288
16.3 Relationship between Electronic Configuration
and Spectroscopic Terms: the Carbon Atom ............... 291
16.4 Spin-orbit Interaction. Fine Structure of the Energy Levels . 295
16.5 Hierarchy of Quantum Numbers. Selection Rules II ........ 302
16.6 Atoms in a Magnetic Field: the Anomalous Zeeman Effect . 306
X Contents
17 Elementary Theory of Scattering
17.1 Introduction...............................................315
17.2 The Cross Section ......................................... 316
17.3 One-Dimensional Case.....................................317
17.4 Three-Dimensional Case ................................... 320
17.5 The Optical Theorem......................................325
17.6 Central Potential .......................................... 326
17.7 Applications...............................................330
17.8 Collision of Identical Particles ............................. 333
17.9 The Reciprocity Theorem and the Detailed Balance........334
18 The Paradoxes of Quantum Mechanics
18.1 Introduction...............................................337
18.2 The de Broglie Box........................................338
18.3 Schrodinger s Cat..........................................340
18.4 What Is a Measurement? .................................. 341
18.5 The Einstein Podolsky-Rosen Paradox .................... 343
18.6 Bell s Theorem ............................................ 345
Appendix - Physical Constants .............................. 349
Index ........................................................... 351
|
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| bvnumber | BV042976769 |
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| language | English |
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| spelling | Picasso, Luigi E. Verfasser (DE-588)1015678548 aut Lectures in quantum mechanics a two-term course Luigi E. Picasso Cham Springer [2016] © 2016 X, 354 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier UNITEXT for physics Quantenmechanik (DE-588)4047989-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenmechanik (DE-588)4047989-4 s DE-604 Erscheint auch als Online-Ausgabe 978-3-319-22632-3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028402419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Picasso, Luigi E. Lectures in quantum mechanics a two-term course Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4123623-3 |
| title | Lectures in quantum mechanics a two-term course |
| title_auth | Lectures in quantum mechanics a two-term course |
| title_exact_search | Lectures in quantum mechanics a two-term course |
| title_full | Lectures in quantum mechanics a two-term course Luigi E. Picasso |
| title_fullStr | Lectures in quantum mechanics a two-term course Luigi E. Picasso |
| title_full_unstemmed | Lectures in quantum mechanics a two-term course Luigi E. Picasso |
| title_short | Lectures in quantum mechanics |
| title_sort | lectures in quantum mechanics a two term course |
| title_sub | a two-term course |
| topic | Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantenmechanik Lehrbuch |
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