Nonrelativistic quantum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2002
|
| Ausgabe: | 3. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index. |
| Beschreibung: | XVII, 522 S. graph. Darst. |
| ISBN: | 981024634X 9789810246518 |
Internformat
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| 100 | 1 | |a Capri, Anton Z. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonrelativistic quantum mechanics |c Anton Z. Capri |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Singapore |b World Scientific |c 2002 | |
| 300 | |a XVII, 522 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index. | ||
| 650 | 7 | |a Kwantummechanica |2 gtt | |
| 650 | 7 | |a Storingsrekening |2 gtt | |
| 650 | 4 | |a Nonrelativistic quantum mechanics | |
| 650 | 4 | |a Perturbation (Quantum dynamics) | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009920544 | ||
Datensatz im Suchindex
| _version_ | 1804129370879557632 |
|---|---|
| adam_text | Contents
The Breakdown of Classical Mechanics
1
1.1
Introduction
.............................. 1
1.2
Blackbody
Radiation
......................... 2
1.3
Stability of Atoms: Discrete Spectral Lines
............ 5
1.4
Photoelectric Effect
.......................... 7
1.5
Wave Particle Duality
........................ 9
1.5.1
Reflection
........................... 9
1.5.2
Refraction
........................... 10
1.6 de Broglie s
Hypothesis
....................... 11
1.7
The Compton Effect
......................... 11
1.8
The Davisson-Germer Experiment
................. 13
1.9
The
Franck-Hertz
Effect
....................... 15
1.10
Planck s Radiation Law
....................... 16
1.11
Einstein s Model for Specific Heat
................. 18
1.12
The Debye Model
........................... 19
1.13
Bohr Model and the Hydrogen Atom
................ 20
1.14
Problems
............................... 24
Review of Classical Mechanics
26
2.1
Introduction
.............................. 26
2.2
Classical Mechanics: Particle in One Dimension
.......... 26
2.3
Lagrangian and Hamiltonian Formulation
............. 31
2.4
Contact Transformations: Hamilton-Jacobi Theory
........ 33
2.5
Interpretation of Action-Angle Variables
.............. 39
2.6
Hydrogen Atom: Bohr-Sommerfeld Quantization
......... 40
2.7
The
Schrödinger
Equation
...................... 43
2.8
Problems
............................... 46
Elementary Systems
48
3.1
Introduction
.............................. 48
3.2
Plane Wave Solutions
........................ 49
3.3
Conservation Law for Particles
................... 49
3.4
Young s Double Slit Experiment
.................. 51
3.5
The Superposition Principle and Group Velocity
......... 52
xi
xii CONTENTS
3.6 Formal
Considerations........................
54
3.7
Ambiguities
.............................. 56
3.7.1
Use of Different Coordinate Systems
............ 57
3.7.2
Non-Commutativity
..................... 58
3.8
Interaction with an Electromagnetic Field
............. 59
3.9
Problems
............................... 60
One-Dimensional Problems
63
4.1
Introduction
.............................. 63
4.2
Particle in a Box
........................... 64
4.3
Parity
................................. 66
4.4
Scattering from a Step-Function Potential
............. 67
4.4.1
Boundary Conditions
.................... 68
4.4.2
Particles from the Left
.................... 69
4.4.3
Interpretation of
R
and
S
.................. 71
4.5
Finite Square Well: Bound States
.................. 73
4.6
Tunneling Through a Square Barrier
................ 76
4.6.1
Resonance Transmission
................... 78
4.7
Time Reversal
............................. 79
4.8
Problems
............................... 80
More One-Dimensional Problems
84
5.1
Introduction
.............................. 84
5.2
General Considerations
........................ 84
5.3
The Simple Harmonic Oscillator
.................. 87
5.3.1
Generating Function for Hermite Polynomials
....... 90
5.3.2
Rodrigues
Formula for Hermite Polynomials
........ 91
5.3.3
Normalization
......................... 92
5.4
The Delta Function
.......................... 93
5.5
Attractive Delta Function Potential
................. 95
5.6
Repulsive Delta Function Potential
................. 97
5.7
Square Well: Scattering and Phase Shifts
............. 98
5.8
Periodic Potentials
.......................... 100
5.8.1
Floquet s Theorem
...................... 101
5.8.2
Bloch s Theorem
....................... 102
5.9
The Kronig-Penney Problem
.................... 103
5.10
Problems
............................... 105
Mathematical Foundations
108
6.1
Introduction
.............................. 108
6.2
Geometry of Hubert Space
...................... 108
6.3
£2: A Model Hubert Space
.....................
Ш
6.4
Operators on
Hubert
Space: Mainly Definitions
.......... 113
6.5
Cayley Transform: Self-Adjoint Operators
............. 118
6.6
Some Properties of Self-Adjoint Operators
............. 122
6.7
Classification of Symmetric Operators
............... 124
CONTENTS xiii
6.8
Spontaneously Broken Symmetry
.................. 132
6.9
Problems
............................... 135
7
Physical Interpretation.
138
7.1
Introduction
.............................. 138
7.2
Al
-
Physical States
......................... 138
7.3
A2
-
Observables
........................... 139
7.4 A3 -
Probabilities
........................... 139
7.5 A4 -
Reduction of the Wave Packet
................. 143
7.5.1
Example
............................ 143
7.6
Compatibility Theorem and Uncertainty Principle
........ 145
7.7
The
Heisenberg
Microscope
..................... 146
7.8
A5
-
The
Schrödinger
Equation
................... 149
7.9
Time Evolution: Constants of the Motion
............. 151
7.10
Time-Energy Uncertainty Relation
................. 152
7.11
Time Evolution of Probability Amplitudes
............. 154
7.12
Problems
............................... 157
8
Distributions and Fourier Transforms
161
8.1
Introduction
.............................. 161
8.2
Functional
.............................. 161
8.3
Fourier Transforms
.......................... 166
8.4
Rigged Hubert Spaces
........................ 168
8.5
Problems
............................... 170
9
Algebraic Methods
173
9.1
Introduction
.............................. 173
9.2
Simple Harmonic Oscillator
..................... 173
9.2.1
Expectation Values
...................... 179
9.3
The Rigid Rotator
.......................... 181
9.4 3D
Rigid Rotator: Angular Momentum
.............. 186
9.5
Algebraic Approach to Angular Momentum
............ 188
9.6
Rotations and Rotational
Invariance
................ 195
9.7
Spin Angular Momentum
...................... 199
9.8
Problems
............................... 202
10
Central Force Problems
207
10.1
Introduction
.............................. 207
10.2
The Radial Equation
......................... 207
10.3
Infinite Square Well
......................... 210
10.4
Simple Harmonic Oscillator: Cartesian Coordinates
....... 212
10.4.1
Degeneracy
........................... 213
10.5
Simple Harmonic Oscillator: Spherical Coordinates
....... 213
10.6
The Hydrogenic Atom
........................ 217
10.6.1
Laguerre Polynomials
.................... 220
10.7
Reduction of the Two-Body Problem
................ 224
xiv CONTENTS
10.8 Problems...............................226
11
Transformation Theory
228
11.1
Introduction.............................
228
11.2
Rotations in a Vector Space
....................228
11.2.1
Fourier Transform of Hermite Functions
.........231
11.3
Dirac Notation
...........................232
11.4
Coherent States
...........................236
11.4.1
The Forced Simple Harmonic Oscillator
.........239
11.5
Quasi-classical States
........................240
11.6
Squeezed States
...........................243
11.7
Example: Angular Momentum
...................246
11.8 Schrödinger
Picture
.........................249
11.9 Heisenberg
Picture
.........................250
11.10
Dirac or Interaction Picture
....................253
11.11
Hidden Variables
..........................256
11.12
Problems
...............................262
12
Non-Degenerate Perturbation Theory
265
12.1
Introduction
............................. 265
12.2 Rayleigh-Schrödinger
Perturbation Theory
............ 266
12.3
First Order Perturbations
..................... 268
12.4
Anharmonic Oscillator
....................... 269
12.5
Ground State of Helium-like Ions
................. 270
12.6
Second Order Perturbations
.................... 272
12.7
Displaced Simple Harmonic Oscillator
............... 273
12.8
Non-degenerate Perturbations to all Orders
........... 275
12.9
Sum Rule: Second Order Perturbation
.............. 278
12.10
Linear Stark Effect
......................... 281
12.11
Problems
............................... 283
13
Degenerate Perturbation Theory
287
13.1
Introduction
............................. 287
13.2
Two Levels:
Rayleigh-Schrödinger
Method
............. 287
13.3 Rayleigh-Schrödinger:
Degenerate Levels
............. 292
13.4
Example: Spin Hamiltonian
.................... 294
13.4.1
Exact Solution
........................ 294
13.4.2 Rayleigh-Schrödinger
Solution
................ 295
13.5
Problems
............................... 296
14
Further Approximation Methods
299
14.1
Introduction
.............................299
14.2
Rayleigh-Ritz Method
.......................300
14.3
Example: Simple Harmonic Oscillator
...............303
14.4
Example: He Ground State
....................303
14.5
The WKB Approximation
...................304
CONTENTS xv
14.5.1
Turning
points
........................ 309
14.6
WKB Applied
to a Potential Well.................
313
14.6.1
Special Boundaries
...................... 315
14.7
WKB Approximation for Tunneling
................ 316
14.8
Alpha Decay
............................. 318
14.8.1
Heuristic Discussion
..................... 318
14.8.2
Detailed Analysis
....................... 322
14.9
Problems
............................... 326
15
Time-Dependent Perturbation Theory
329
15.1
Introduction
.............................329
15.2
Formal Considerations
.......................329
15.3
Transition Amplitudes
.......................332
15.4
Time-Independent Perturbation
..................333
15.5
Periodic Perturbation of Finite Duration
.............335
15.6
Photo-Ionization of Hydrogen Atom
................338
15.7
The Adiabatic Approximation
...................341
15.8
The Sudden Approximation
....................345
15.9 Dipole
in a Time-Dependent Magnetic Field
...........347
15.9.1
Oscillatory Perturbation
...................348
15.9.2
Slowly Varying Perturbation
................349
15.9.3
Sudden Approximation
...................351
15.10
Two-Level Systems
.........................352
15.11
Berry s Phase
............................355
15.12
Problems
...............................358
16
Particle in a Uniform Magnetic Field
362
16.1
Introduction
.............................362
16.2
Gauge Transformations
.......................362
16.3
Motion in a Uniform Magnetic Field
...............366
16.3.1
Classical Hall Effect
.....................366
16.3.2
Landau Levels
........................368
16.4
Crossed Electric and Magnetic Fields
...............369
16.4.1
The Quantum Hall Effect
..................371
16.5
Magnetic Field:
Heisenberg
Equations
..............372
16.6
Energy Eigenfunctions
.......................375
16.7
Translation Invariant States
....................378
16.8
Gauge Transformations
.......................381
16.9
Problems
...............................383
17
Applications
385
17.1
Introduction
.............................385
17.2
Spin and Spin-Orbit Coupling
...................385
17.3
Alkali Spectra
............................387
17.4
Addition of Angular Momenta
...................388
17.5
Two Spin States
.........................391
xvi
CONTENTS
17.6
Spin I
+
Orbital Angular Momentum
.............. 392
17.7
The Weak-Field
Zeeman
Effect
.................. 393
17.8
The Aharonov-Bohm Effect
.................... 396
17.9
Problems
............................... 399
18
Scattering Theory
-
Time Dependent
403
18.1
Introduction
.............................403
18.2
Classical Scattering Theory
....................404
18.3
Asymptotic States:
Schrödinger
Picture
.............405
18.4
The M0ller Wave Operators
....................406
18.5
Green s Functions and Propagators
................408
18.6
Integral Equations for Propagators
................411
18.7
Cross-Sections
............................412
18.8
The Lippmann-Schwinger Equations
...............414
18.9
The S-Matrix and the Scattering Amplitude
...........415
18.10
Problems
...............................418
19
Scattering Theory
-
Time Independent
420
19.1
Introduction
.............................420
19.2
The Scattering Amplitude
.....................420
19.3
Green s Functions
..........................422
19.4
The Born Approximation
......................425
19.5
The Yukawa Potential
.......................427
19.6
Free Particle in Spherical Coordinates
..............428
19.7
Partial Wave Analysis
.......................433
19.8
Phase Shifts
.............................435
19.9
The Optical Theorem: Unitarity Bound
.............437
19.10
Partial Waves: Lippmann-Schwinger Equation
..........438
19.11
Effective Range Approximation
..................440
19.12
Resonant Scattering
.........................444
19.13
Problems
...............................447
20
Systems of Identical Particles
452
20.1
Introduction
............................. 452
20.2
Two Identical Particles
....................... 453
20.3
The Hydrogen Molecule
...................... 454
20.4 N
Identical Particles
........................ 459
20.5
Non-Interacting
Fermions
..................... 461
20.6
Non-Interacting Bosons
....................... 462
20.7
TV-Space: Second Quantization for Bosons
............ 463
20.8
JV-Space: Second Quantization for
Fermions
........... 466
20.9
Field Operators in the
Schrödinger
Picture
............ 469
20.10
Representation of Operators
.................... 472
20.11 Heisenberg
Picture
........... 475
20.12
Problems
.......................... . . . . . 477
CONTENTS xvii
21 Quantum
Statistical Mechanics
482
21.1
Introduction
............................. 482
21.2
The Density Matrix
......................... 483
21.2.1
The Microcanonical Ensemble
................ 483
21.2.2
The Canonical Ensemble
................... 485
21.2.3
The Grand Canonical Ensemble
.............. 486
21.3
The Ideal Gases
........................... 487
21.4
General Properties of the Density Matrix
............. 492
21.5
The Density Matrix and Polarization
............... 495
21.6
Composite Systems
......................... 497
21.7 von
Neumann s Theory of Measurement
............. 499
21.8
Decoherence
............................. 503
21.9
Conclusion
.............................. 508
21.10
Problems
............................... 509
Index
515
|
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| id | DE-604.BV014595685 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:04Z |
| institution | BVB |
| isbn | 981024634X 9789810246518 |
| language | English |
| lccn | 2002028870 |
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| owner_facet | DE-91G DE-BY-TUM DE-29T DE-11 DE-355 DE-BY-UBR |
| physical | XVII, 522 S. graph. Darst. |
| publishDate | 2002 |
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| publishDateSort | 2002 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Capri, Anton Z. Verfasser aut Nonrelativistic quantum mechanics Anton Z. Capri 3. ed. Singapore World Scientific 2002 XVII, 522 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index. Kwantummechanica gtt Storingsrekening gtt Nonrelativistic quantum mechanics Perturbation (Quantum dynamics) Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009920544&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Capri, Anton Z. Nonrelativistic quantum mechanics Kwantummechanica gtt Storingsrekening gtt Nonrelativistic quantum mechanics Perturbation (Quantum dynamics) Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 |
| title | Nonrelativistic quantum mechanics |
| title_auth | Nonrelativistic quantum mechanics |
| title_exact_search | Nonrelativistic quantum mechanics |
| title_full | Nonrelativistic quantum mechanics Anton Z. Capri |
| title_fullStr | Nonrelativistic quantum mechanics Anton Z. Capri |
| title_full_unstemmed | Nonrelativistic quantum mechanics Anton Z. Capri |
| title_short | Nonrelativistic quantum mechanics |
| title_sort | nonrelativistic quantum mechanics |
| topic | Kwantummechanica gtt Storingsrekening gtt Nonrelativistic quantum mechanics Perturbation (Quantum dynamics) Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Kwantummechanica Storingsrekening Nonrelativistic quantum mechanics Perturbation (Quantum dynamics) Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009920544&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT capriantonz nonrelativisticquantummechanics |