Quantum physics in the nanoworld: Schrödinger's cat and the Dwarfs
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2015
|
| Edition: | 2. ed. |
| Series: | Graduate texts in physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 508 S. Ill., graph. Darst. |
| ISBN: | 9783319146683 |
| ISSN: | 1868-4513 |
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| 245 | 1 | 0 | |a Quantum physics in the nanoworld |b Schrödinger's cat and the Dwarfs |c Hans Lüth |
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Record in the Search Index
| _version_ | 1804174868692860928 |
|---|---|
| adam_text | Titel: Quantum physics in the Nanoworld
Autor: Lüth, Hans
Jahr: 2015
Contents
1 Introduction........................................ 1
1.1 General and Historical Remarks...................... 1
1.2 Importance for Science and Technology................. 3
1.3 Philosophical Implications.......................... 5
References.......................................... 8
2 Some Fundamental Experiments......................... 9
2.1 Photoelectric Effect............................... 9
2.2 Compton Effect................................. 12
2.3 Diffraction of Massive Particles...................... 15
2.4 Particle Interference at the Double Slit.................. 21
2.4.1 Double Slit Experiments with Electrons........... 21
2.4.2 Particle Interference and Which-Way
Information.............................. 24
References.......................................... 27
3 Particle-Wave Duality................................. 29
3.1 The Wave Function and Its Interpretation............... 29
3.2 Wave Packet and Particle Velocity.................... 33
3.3 The Uncertainty Principle.......................... 37
3.4 An Excursion into Classical Mechanics................. 39
3.5 Observables, Operators and Schrödinger Equation.......... 42
3.6 Simple Solutions of the Schrödinger Equation............ 48
3.6.1 Locked-Up Electrons: Confined Quantum States ... 49
3.6.2 Particle Currents........................... 56
3.6.3 Electrons Run Against a Potential Step........... 58
3.6.4 Electrons Tunnel Through a Barrier............. 61
3.6.5 Resonant Tunneling........................ 66
3.7 Single Electron Tunneling.......................... 75
3.8 The Quantum Point Contact as Charge Detector........... 82
References.......................................... 88
xii Contents
4 Quantum States in Hubert Space......................... 89
4.1 Eigenvectors and Measurement of Observables............ 89
4.2 Commutation of Operators: Commutators............... 95
4.3 Representation of Quantum States and Observables......... 97
4.3.1 Vectors of Probability Amplitudes and Matrices
as Operators............................. . 97
4.3.2 Rotations of Hubert Space.................... 103
4.3.3 Quantum States in Dirac Notation............... 106
4.3.4 Quantum States with a Continuous
Eigenvalue Spectrum........................ 110
4.3.5 Time Evolution in Quantum Mechanics........... 115
4.4 Games with Operators: The Oscillator.................. 118
4.4.1 The Classical Harmonie Oscillator.............. 118
4.4.2 Upstairs-Downstairs: Step Operators
and Eigenvalues........................... 119
4.4.3 The Anharmonic Oscillator................... 126
References.......................................... 130
5 Angular Momentum, Spin and Particle Categories............ 131
5.1 The Classical Circular Motion....................... 131
5.2 Quantum Mechanical Angular Momentum............... 133
5.3 Rotational Symmetry and Angular Momentum; Eigenstates . . . 140
5.4 Circulating Electrons in a Magnetic Field................ 147
5.4.1 The Lorentz Force......................... 147
5.4.2 The Hamilton Operator with Magnetic Field....... 148
5.4.3 Angular Momentum and Magnetic Moment........ 150
5.4.4 Gauge Invariance and Aharanov-Bohm-Effect...... 153
5.5 The Spin...................................... 160
5.5.1 Stern-Gerlach Experiment.................... 160
5.5.2 The Spin and Its 2D Hubert Space.............. 164
5.5.3 Spin Precession........................... 168
5.6 Particle Categories: Fermions and Bosons............... 171
5.6.1 Two and More Particles...................... 171
5.6.2 Spin and Particle Categories: The Pauli
Exclusion Principle......................... 175
5.6.3 Two Different Worlds: Fermi and Böse Statistics .... 180
5.6.4 The Zoo of Elementary Particles................ 188
5.7 Angular Momentum in Nanostructures and Atoms......... 199
5.7.1 Artificial Quantum Dot Atoms................. 199
5.7.2 Atoms and Periodic Table.................... 206
5.7.3 Quantum Rings........................... 211
References.......................................... 215
Contents
Approximate Solutions for Important Model Systems.......... 217
6.1 Particles in a Weakly Varying Potential: The WKB Method. . . 218
6.1.1 Application: Tunneling Through a Schottky Barrier. . . 220
6.2 Clever Guess of a Wave Function: The Variational Method . . . 223
6.2.1 Example of the Harmonie Oscillator............. 226
6.2.2 The Ground State of the Hydrogen Atom.......... 229
6.2.3 Molecules and Coupled Quantum Dots........... 232
6.2.4 Experimental Realisation of a Quantum
Dot Molecule............................. 240
6.3 Small Stationary Potential Perturbations:
The Time-Independent Perturbation Method.............. 244
6.3.1 Perturbation of Degenerate States............... 248
6.3.2 Example: The Stark Effect in a Semiconductor
Quantum Well............................ 251
6.4 Transitions Between Quantum States:
The Time-Dependent Perturbation Method............... 254
6.4.1 Periodic Perturbation: Fermi s Golden Rule........ 256
6.4.2 Electron-Light Interaction: Optical Transitions...... 259
6.4.3 Optical Absorption and Emission
in a Quantum Well......................... 262
6.4.4 Dipole Selection Rules for Angular
Momentum States.......................... 265
6.5 Electronic Transitions in 2-Level Systems:
The Rotating Wave Approximation.................... 272
6.5.1 2-Level Systems in Resonance
with Electromagnetic Radiation................ 272
6.5.2 Spin Flip................................ 277
6.5.3 Nuclear Spin Resonance in Chemistry,
Biology and Medicine....................... 282
6.6 Scattering of Particles............................. 288
6.6.1 Scattered Waves and Differential
Scattering Cross Section..................... 290
6.6.2 Scattering Amplitude and Born Approximation...... 292
6.6.3 Coulomb Scattering......................... 297
6.6.4 Scattering on Crystals, on Surfaces
and on Nanostructures....................... 301
6.6.5 Inelastic Scattering on a Molecule............... 309
References.......................................... 313
Superposition, Entanglement and Other Oddities............. 315
7.1 Superposition of Quantum States..................... 316
7.1.1 Scattering of Two Identical Particles:
A Special Superposition State.................. 318
xiv Contents
7.2 Entanglement................................... 322
7.2.1 BelFs Inequality and Its Experimental Check....... 327
7.2.2 Which Way Information and Entanglement:
A Gedanken Experiment..................... 334
7.2.3 Which Way Probing in an Aharanov-Bohm
Interference Experiment...................... 338
7.3 Pure and Mixed States: The Density Matrix.............. 343
7.3.1 Quantum Mechanical and Classical Probabilities..... 343
7.3.2 The Density Matrix......................... 347
7.4 Quantum Environment, Measurement Process
and Entanglement................................ 351
7.4.1 Subsystem and Environment.................. 351
7.4.2 Open Quantum Systems, Decoherence
and Measurement Process.................... 354
7.4.3 Schrödinger s Cat.......................... 359
7.5 Superposition States for Quantum-Bits
and Quantum Computing........................... 360
7.5.1 Coupled Quantum Dots as Quantum-Bits.......... 361
7.5.2 Experimental Realization of a Quantum-Bit
by Quantum Dots.......................... 365
References.......................................... 370
8 Fields and Quanta................................... 373
8.1 Ingredients of a Quantum Field Theory................. 374
8.2 Quantization of the Electromagnetic Field............... 376
8.2.1 What Are Photons?......................... 383
8.2.2 2-Level Atom in the Light Field:
Spontaneous Emission....................... 387
8.2.3 Atom Diffraction by Light Waves............... 393
8.2.4 Once Again: Which Way Information
and Entanglement.......................... 399
8.2.5 The Casimir Effect......................... 404
8.3 The Quantized Schrödinger Field of Massive Particles....... 407
8.3.1 The Quantized Fermionic Schrödinger Field........ 414
8.3.2 Field Operators and Back to the Single
Particle Schrödinger Equation.................. 418
8.3.3 The Particle Picture in Quantum Field Theory...... 424
8.3.4 Electrons in Crystals: Back to the Single
Particle Approximation...................... 426
8.3.5 The Band Model: Metals and Semiconductors...... 430
Contents xv
8.4 Quantized Lattice Waves: Phonons.................... 439
8.4.1 Phonon-Phonon Interaction................... 448
8.4.2 Electron-Phonon Interaction................... 453
8.4.3 Absorption and Emission of Phonons............ 457
8.4.4 Field Quanta Mediate Forces Between Particles..... 460
References.......................................... 465
9 Synopsis........................................... 467
Appendix A: Interfaces and Heterostructures................... 471
Appendix B: Preparation of Semiconductor Nanostructures........ 479
Appendix C: The Reduced Density Matrix..................... 489
Problems.............................................. 493
Index................................................ 505
|
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| dewey-ones | 530 - Physics |
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| discipline | Physik |
| edition | 2. ed. |
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| id | DE-604.BV042676446 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:07:14Z |
| institution | BVB |
| isbn | 9783319146683 |
| issn | 1868-4513 |
| language | English |
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| physical | XV, 508 S. Ill., graph. Darst. |
| publishDate | 2015 |
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| publisher | Springer |
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| spelling | Lüth, Hans 1940- Verfasser (DE-588)121512746 aut Quantenphysik in der Nanowelt Quantum physics in the nanoworld Schrödinger's cat and the Dwarfs Hans Lüth 2. ed. Cham [u.a.] Springer 2015 XV, 508 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics 1868-4513 Physics Quantum theory Nanotechnology Quantum Physics Nanoscale Science and Technology Solid State Physics Particle and Nuclear Physics Quantentheorie Quantenphysik (DE-588)4266670-3 gnd rswk-swf Quantenphysik (DE-588)4266670-3 s DE-604 Erscheint auch als Online-Ausgabe 978-3-319-14669-0 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028108379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lüth, Hans 1940- Quantum physics in the nanoworld Schrödinger's cat and the Dwarfs Physics Quantum theory Nanotechnology Quantum Physics Nanoscale Science and Technology Solid State Physics Particle and Nuclear Physics Quantentheorie Quantenphysik (DE-588)4266670-3 gnd |
| subject_GND | (DE-588)4266670-3 |
| title | Quantum physics in the nanoworld Schrödinger's cat and the Dwarfs |
| title_alt | Quantenphysik in der Nanowelt |
| title_auth | Quantum physics in the nanoworld Schrödinger's cat and the Dwarfs |
| title_exact_search | Quantum physics in the nanoworld Schrödinger's cat and the Dwarfs |
| title_full | Quantum physics in the nanoworld Schrödinger's cat and the Dwarfs Hans Lüth |
| title_fullStr | Quantum physics in the nanoworld Schrödinger's cat and the Dwarfs Hans Lüth |
| title_full_unstemmed | Quantum physics in the nanoworld Schrödinger's cat and the Dwarfs Hans Lüth |
| title_short | Quantum physics in the nanoworld |
| title_sort | quantum physics in the nanoworld schrodinger s cat and the dwarfs |
| title_sub | Schrödinger's cat and the Dwarfs |
| topic | Physics Quantum theory Nanotechnology Quantum Physics Nanoscale Science and Technology Solid State Physics Particle and Nuclear Physics Quantentheorie Quantenphysik (DE-588)4266670-3 gnd |
| topic_facet | Physics Quantum theory Nanotechnology Quantum Physics Nanoscale Science and Technology Solid State Physics Particle and Nuclear Physics Quantentheorie Quantenphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028108379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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