Quantum mechanics: fundamentals
Gespeichert in:
Hauptverfasser: | , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York, NY [u.a.]
Springer
2004
|
Ausgabe: | 2. ed., 1. softcover print. |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XVII, 620 S. |
ISBN: | 0387220232 9780387220239 |
Internformat
MARC
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100 | 1 | |a Gottfried, Kurt |d 1929-2022 |e Verfasser |0 (DE-588)135940001 |4 aut | |
245 | 1 | 0 | |a Quantum mechanics |b fundamentals |c Kurt Gottfried ; Tung-Mow Yan |
250 | |a 2. ed., 1. softcover print. | ||
264 | 1 | |a New York, NY [u.a.] |b Springer |c 2004 | |
300 | |a XVII, 620 S. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
650 | 7 | |a Mecânica quântica |2 larpcal | |
650 | 4 | |a Quantentheorie | |
650 | 4 | |a Quantum theory | |
650 | 4 | |a Yan, Tung-mow | |
650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
689 | 0 | 0 | |a Quantenmechanik |0 (DE-588)4047989-4 |D s |
689 | 0 | |5 DE-604 | |
700 | 1 | |a Yan, Tung-Mow |e Verfasser |4 aut | |
856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012846110&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
999 | |a oai:aleph.bib-bvb.de:BVB01-012846110 |
Datensatz im Suchindex
_version_ | 1804132827876294656 |
---|---|
adam_text | Contents
Preface
vu
Fundamental
Concepts
1
1.1
Complementarity and Uncertainty
................... 1
(a) Complementarity
2
(b) The Uncertainty Principle
6
1.2
Superposition
............................... 11
(a) The Superposition Principle
11
(b) Two-Particle States
12
(c) Two-Particle
Interferometry
1Ą
(d) E
PR Correlations
19
1.3
The Discovery of Quantum Mechanics
................. 20
1.4
Problems
................................. 24
The Formal Framework
27
2.1
The Formal Language: Hubert Space
.................. 27
(a) Hubert
Space
29
(b) Dirac s Notation
30
(c) Operators
32
(d) Unitary Transformations
35
(e) Eigenvalues and Eigenvectors
38
2.2
States and Probabilities
......................... 39
(a) Quantum States
Ą0
(b) Measurement Outcomes
A3
(c) Mixtures and the Density Matrix
Ą6
(d) Entangled States
50
(e) The Wigner Distribution
52
2.3
Canonical Quantization
......................... 54
(a) The Canonical Commutation Rules
5Ą
(b)
Schrődinger
Wave Functions
56
(c) Uncertainty Relations
59
2.4
The Equations of Motion
........................ 60
(a) The
Schrődinger
Picture
60
(b) The
Heisenberg
Picture
65
(c) Time Development of Expectation Values
66
(d) Time-Energy Uncertainty
67
(e) The Interaction Picture
70
2.5
Symmetries and Conservation Laws
................... 71
(a) Symmetries and Unitary Transformations
72
(b) Spatial Translations
73
xii Contents
(c)
Symmetry Groups
74
(d)
Rotations
76
(e)
Space Reflection and Parity
81
(f) Gauge
Invariance
82
2.6
Propagators and Green s Functions
................... 84
(a) Propagators
8Ą
(b) Green s Functions
85
(c) The Free Particle Propagator and Green s Function
87
(d) Perturbation Theory
89
2.7
The Path Integral
............................ 92
(a) The Feynman Path Integral
92
(b) The Free-Particle Path Integral
95
2.8
Semiclassical Quantum Mechanics
................... 98
(a) Hamilton-
J
acobi Theory
99
(b) The Semiclassical Wave Function
102
(c) The Semiclassical Propagator
104
(d) Derivations
106
2.9
Problems
.................................109
Endnotes
111
3
Basic Tools
113
3.1
Angular Momentum: The Spectrum
..................113
3.2
Orbital Angular Momentum
.......................116
3.3
Spin
....................................120
(a) Spin |
121
(b) Spin
1 125
(c) Arbitrary Spins
127
3.4
Free-Particle States
............................128
3.5
Addition of Angular Momenta
......................133
(a) General Results
133
(b) Adding Spins j) and Unit Spins
135
(c) Arbitrary Angular Momenta; Clebsch-Gordan Coefficients
137
(d) Matrix Elements of Vector Operators
1Ą0
3.6
The Two-Body Problem
.........................142
(a) Center-of-Mass and Relative Motion
Ц2
(b) The Radial
Schrödinger
Equation: General Case
Ц4
(c) Bound-State Coulomb Wave Functions
1Ą7
3.7
Basic Approximation Methods
.....................149
(a) Stationary-State Perturbation Theory
150
(b) Degenerate-State Perturbation Theory
153
(c) Time-Dependent Perturbation Theory
156
(d) The Golden Rule
159
(e) The Variational Principle
161
3.8
Problems
.................................162
4
Low-Dimensional Systems
165
4.1
Spectroscopy in Two-Level Systems
...................166
(a) Level Crossings
166
(b) Resonance Spectroscopy
169
Contents xiii
4.2
The Harmonic Oscillator
.........................174
(a) Equations of Motion
17Ą
(b) Energy Eigenvalues and
Eigen)
unctions
175
(c) The Forced Oscillator
178
(d) Coherent States
181
(e) Wigner Distributions
184
(f) Propagator and Path Integral
186
4.3
Motion in a Magnetic Field
.......................188
(a) Equations of Motion and Energy Spectrum
188
(b) Eigenstates of Energy and Angular Momentum
190
(c) Coherent States
19Ą
(d) The Aharonov-Bohm Effect
196
4.4
Scattering in One Dimension
......................198
(a) General Properties
198
(b) The Delta-Function Potential
202
(c) Resonant Transmission and Reflection
204
(d) The Exponential Decay Law
213
4.5
The Semiclassical Approximation
....................216
(a) The WKB Approximation
217
(b) Connection Formulas
218
(c) Energy Eigenvalues, Barrier Transmission, and ex-Decay
222
(d) Exactly Solvable Examples
225
4.6
Problems
.................................228
Endnotes 233
Hydrogenic Atoms
235
5.1
Qualitative Overview
...........................235
5.2
The Kepler Problem
...........................238
(a) The
Lenz
Vector
238
(b) The Energy Spectrum
240
(c) The Conservation of
M
242
(d)
Wave Functions
243
5.3
Fine and Hyperfine Structure
......................245
(a) Fine Structure
245
(b) Hyperfine Structure
—
General Features
249
(c) Magnetic
Dipole Hfs 250
(d) Electric Quadrupole Hfs
252
5.4
The
Zeeman
and Stark Effects
.....................254
(a) Order of Magnitude Estimates
254
(b) The
η
= 2
Multiplet
257
(c)
Strong Fields
260
5.5
Problems
.................................263
Endnotes 266
Two-Electron Atoms
267
6.1
Two Identical Particles
..........................267
(a) Spin and Statistics
267
(b) The Exclusion Principle
269
(c) Symmetric and Antisymmetric States
270
;iv Contents
6.2
The Spectrum of Helium
.........................272
6.3
Atoms with Two Valence Electrons
...................275
(a) The Shell Model and Coupling Schemes
275
(b) The Configuration p2
276
6.4
Problems
.................................279
Endnotes 281
7
Symmetries
283
7.1
Equivalent Descriptions and Wigner s Theorem
............283
7.2
Time Reversal
...............................286
(a) The Time Reversal Operator
287
(b) Spin
0 289
(c) Spin |
290
7.3
Galileo Transformations
.........................292
(a) Transformation of States: Galileo
Invariance
292
(b)
Mass Differences
295
7.4
The Rotation Group
...........................297
(a) The Group SO(3)
297
(b) SO(3) and SU{2)
299
(c) Irreducible Representations of SU{2)
301
(d) D(R) in Terms of
Euler
Angles
304
(e) The
Kronecker
Product
306
(f) Integration over Rotations
307
7.5
Some Consequences of Symmetry
....................311
(a) Rotation of Spherical Harmonics
312
(b)
Helicity
States
ЗЦ
(c) Decay Angular Distributions
316
(d) Rigid-Body Motion
317
7.6
Tensor Operators
.............................320
(a) Definition of Tensor Operators
320
(b) The Wigner-Eckart Theorem
322
(c) Racah Coefficients and 6-j Symbols
32Ą
7.7
Geometric Phases
.............................326
(a) Spin in Magnetic Field
327
(b) Correction to the Adiabatic Approximation
329
7.8
Problems
.................................331
Endnotes 334
8
Elastic Scattering
335
8.1
Consequences of Probability and Angular Momentum Conservation
. 335
(a) Partial Waves
335
(b) Hard Sphere Scattering
З40
(c) Time-Dependent Description and the Optical Theorem
З4О
8.2
General Properties of Elastic Amplitudes
...............345
(a) Integral Equations and the Scattering Amplitude
3Ą6
(b) A
Solvable Example
350
(c) Bound-State Poles
353
(d) Symmetry Properties of the Amplitude
354
(e) Relations Between Laboratory and Center-of-Mass Quantities
356
Contents xv
8.3
Approximations
to Elastic Amplitudes
.................357
(a) The Born Approximation
358
(b) Validity of the Born Approximation
361
(c) Short-Wavelength Approximations
364
8.4
Scattering in a Coulomb Field
......................368
(a) The Coulomb Scattering Amplitude
368
(b) The Influence of a Short-Range Interaction
373
8.5
Scattering of Particles with Spin
....................376
(a) Symmetry Properties
377
(b) Cross Section and Spin Polarization
378
(c) Scattering of a Spin Particle by a Spin
0
Target
379
8.6
Neutron-Proton Scattering and the
Deuteron.............382
(a) Low-Energy Neutron-Proton Scattering
383
(b) The
Deuteron
and Low-Energy np Scattering
385
(c) Neutron Scattering by the Hydrogen Molecule
388
(d) The Tensor Force
390
8.7
Scattering of Identical Particles
.....................392
(a) Boson-Boson Scattering
392
(b) Fermion-Fermion Scattering
395
8.8
Problems
.................................397
9
Inelastic Collisions
403
9.1
Atomic Collision Processes
........................403
(a) Scattering Amplitudes and Cross Sections
ĄOĄ
(b) Elastic Scattering
407
(c) Inelastic scattering
Ą09
(d) Energy Loss
41%
9.2
The
S
Matrix
...............................414
(a) Scattering by a Bound Particle
415
(b) The
S
Matrix
417
(c) Transition Rates and Cross Sections 4%1
9.3
Inelastic Resonances
...........................424
(a) A Solvable Model
424
(b) Elastic and Inelastic Cross Sections 4%8
9.4
Problems
.................................433
Endnotes
4З5
10
Electrodynamics
437
10.1
Quantization of the Free Field
......................437
(a) The Classical Theory
4З8
(b) Quantization
441
(c) Photons
44З
(d) Space Reflection and Time Reversal
448
10.2
Causality and Uncertainty in Electrodynamics
.............450
(a) Commutation Rides: Complementarity
450
(b) Uncertainty Relations
4^2
10.3
Vacuum Fluctuations
...........................454
(a) The
Casimir
Effect
455
(b) The Lamb Shift
458
xvi Contents
10.4
Radiative Transitions
...........................460
(a) The Interaction Between Field and Sources
Ą61
(b) Transition Rates
Ą63
(c)
Dipole
Transitions
Ą66
10.5
Quantum Optics
.............................468
(a) The Beam Splitter
Ą68
(b) Various States of the Field
Ą10
(c) Photon Coincidences
Ą7Ą
10.6
The Photoeffect in Hydrogen
......................476
(a) High Energies
Ą76
(b) The Cross Section Near Threshold
478
10.7
Scattering of Photons
..........................482
10.8
Resonant Scattering and Spontaneous Decay
.............485
(a) Model Hamiltonian
Ą86
(b) The Elastic Scattering Cross Section
Ą88
(c) Decay of the Excited State
492
(d) The Connection Between Self-Energy and Resonance Width
495
10.9
Problems
.................................496
Endnotes 501
11
Systems of Identical Particles
503
11.1
Indistinguishability
............................503
11.2
Second Quantization
...........................506
(a) Bose-Einstein Statistics
507
(b) Fermi-Dirac Statistics
513
(c) The Equations of Motion
516
(d) Distribution Functions
518
11.3
Ideal Gases
................................519
(a) The Grand Canonical Ensemble
520
(b) The Ideal Fermi Gas
521
(c) The Ideal
Bose Gas
524
11.4
The Mean Field Approximation
.....................526
(a) The Dilute Bose-Einstein Condensate
527
(b) The Hartree-Fock Equations
530
11.5
Problems
.................................535
12
Interpretation
539
12.1
The Critique of Einstein,
Podolsky
and Rosen
.............540
12.2
Hidden Variables
.............................544
12.3
Bell s Theorem
..............................546
(a) The Spin Singlet State
547
(b) Bell s Theorem
548
(c) The Clauser-Horne Inequality
550
(d) An Experimental Test of Bell s Inequality
551
12.4
Locality
..................................554
12.5
Measurement
...............................558
(a) A Measurement Device
558
(b) Coherence and Entropy Following Measurement
568
(c) An Optical Analogue to the Stern-Gerlach Experiment
566
Contents xvii
(d)
A Delayed Choice Experiment
570
(e) Summation
572
12.6
Problems
.................................574
Endnotes 575
13
Relativistic Quantum Mechanics
577
13.1
Introduction
................................577
13.2
The Dirac Equation
...........................579
(a) Lorentz
Transformations of Spinors
580
(b) The Free-Particle Dirac Equation
58Ą
(c) Charge and Current Densities
587
13.3
Electromagnetic Interaction of a Dirac Particle
............589
(a) The Dirac Equation in the Presence of a Field
589
(b) The Magnetic Moment
591
(c) The Fine Structure Hamiltonian
593
(d) Antiparticles and Charge Conjugation
595
13.4
Scattering of Ultra-Relativistic Electrons
................597
13.5
Bound States in a Coulomb Field
....................600
13.6
Problems
.................................605
Endnotes 606
Appendix
607
Index
610
|
any_adam_object | 1 |
author | Gottfried, Kurt 1929-2022 Yan, Tung-Mow |
author_GND | (DE-588)135940001 |
author_facet | Gottfried, Kurt 1929-2022 Yan, Tung-Mow |
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author_variant | k g kg t m y tmy |
building | Verbundindex |
bvnumber | BV019383119 |
callnumber-first | Q - Science |
callnumber-label | QC174 |
callnumber-raw | QC174.12 |
callnumber-search | QC174.12 |
callnumber-sort | QC 3174.12 |
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classification_rvk | UK 1000 |
classification_tum | PHY 020f |
ctrlnum | (OCoLC)56830138 (DE-599)BVBBV019383119 |
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dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 530 - Physics |
dewey-raw | 530.12 |
dewey-search | 530.12 |
dewey-sort | 3530.12 |
dewey-tens | 530 - Physics |
discipline | Physik |
edition | 2. ed., 1. softcover print. |
format | Book |
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id | DE-604.BV019383119 |
illustrated | Not Illustrated |
indexdate | 2024-07-09T19:59:01Z |
institution | BVB |
isbn | 0387220232 9780387220239 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012846110 |
oclc_num | 56830138 |
open_access_boolean | |
owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-634 DE-188 |
owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-11 DE-634 DE-188 |
physical | XVII, 620 S. |
publishDate | 2004 |
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publishDateSort | 2004 |
publisher | Springer |
record_format | marc |
spelling | Gottfried, Kurt 1929-2022 Verfasser (DE-588)135940001 aut Quantum mechanics fundamentals Kurt Gottfried ; Tung-Mow Yan 2. ed., 1. softcover print. New York, NY [u.a.] Springer 2004 XVII, 620 S. txt rdacontent n rdamedia nc rdacarrier Mecânica quântica larpcal Quantentheorie Quantum theory Yan, Tung-mow Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Yan, Tung-Mow Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012846110&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Gottfried, Kurt 1929-2022 Yan, Tung-Mow Quantum mechanics fundamentals Mecânica quântica larpcal Quantentheorie Quantum theory Yan, Tung-mow Quantenmechanik (DE-588)4047989-4 gnd |
subject_GND | (DE-588)4047989-4 |
title | Quantum mechanics fundamentals |
title_auth | Quantum mechanics fundamentals |
title_exact_search | Quantum mechanics fundamentals |
title_full | Quantum mechanics fundamentals Kurt Gottfried ; Tung-Mow Yan |
title_fullStr | Quantum mechanics fundamentals Kurt Gottfried ; Tung-Mow Yan |
title_full_unstemmed | Quantum mechanics fundamentals Kurt Gottfried ; Tung-Mow Yan |
title_short | Quantum mechanics |
title_sort | quantum mechanics fundamentals |
title_sub | fundamentals |
topic | Mecânica quântica larpcal Quantentheorie Quantum theory Yan, Tung-mow Quantenmechanik (DE-588)4047989-4 gnd |
topic_facet | Mecânica quântica Quantentheorie Quantum theory Yan, Tung-mow Quantenmechanik |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012846110&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT gottfriedkurt quantummechanicsfundamentals AT yantungmow quantummechanicsfundamentals |