Quantum mechanics: concepts and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2009
|
| Ausgabe: | 2nd edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 671 S. Ill., graph. Darst. |
| ISBN: | 9780470026793 9780470026786 |
Internformat
MARC
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| 020 | |a 9780470026793 |c pbk. |9 978-0-470-02679-3 | ||
| 020 | |a 9780470026786 |c hbk. |9 978-0-470-02678-6 | ||
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| 035 | |a (DE-599)BVBBV035245888 | ||
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| 100 | 1 | |a Zettili, Nouredine |d 19XX- |e Verfasser |0 (DE-588)137660839 |4 aut | |
| 245 | 1 | 0 | |a Quantum mechanics |b concepts and applications |c Nouredine Zettili |
| 250 | |a 2nd edition | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2009 | |
| 300 | |a XVI, 671 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory | |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017051606 | ||
Datensatz im Suchindex
| _version_ | 1804138524977397760 |
|---|---|
| adam_text | Contents
Preface
to the Second Edition
xiii
Preface to the First Edition
xv
Note to the Student
xvi
1
Origins of Quantum Physics
1
1.1
Historical Note
.................................. 1
1.2
Particle Aspect of Radiation
........................... 4
1.2.1
Blackbody
Radiation
........................... 4
1.2.2
Photoelectric Effect
............................ 10
1.2.3
Compton Effect
.............................. 13
1.2.4
Pair Production
.............................. 16
1.3
Wave Aspect of Particles
............................. 18
1.3.1 de
Brogue s Hypothesis: Matter Waves
................. 18
1.3.2
Experimental Confirmation of
de
Brogue s Hypothesis
......... 18
1.3.3
Matter Waves for Macroscopic Objects
................. 20
1.4
Particles versus Waves
.............................. 22
1.4.1
Classical View of Particles and Waves
.................. 22
1.4.2
Quantum View of Particles and Waves
.................. 23
1.4.3
Wave-Particle Duality: Complementarity
................ 26
1.4.4
Principle of Linear Superposition
.................... 27
1.5
Indeterministic Nature of the Microphysical World
............... 27
1.5.1
Heisenberg s Uncertainty Principle
................... 28
1.5.2
Probabilistic Interpretation
........................ 30
1.6
Atomic Transitions and Spectroscopy
...................... 30
1.6.1
Rutherford Planetary Model of the Atom
................ 30
1.6.2
Bohr Model of the Hydrogen Atom
................... 31
1.7
Quantization Rules
................................ 36
1.8
Wave Packets
................................... 38
1.8.1
Localized Wave Packets
......................... 39
1.8.2
Wave Packets and the Uncertainty Relations
............... 42
1.8.3
Motion of Wave Packets
......................... 43
1.9
Concluding Remarks
............................... 54
1.10
Solved Problems
................................. 54
1.11
Exercises
..................................... 71
vi
CONTENTS
1
Mathematical Tools of
Quantum
Mechanics
79
2.1
Introduction
.................................... 79
2.2
The
Hüben
Space and Wave Functions
...................... 79
2.2.1
The Linear Vector Space
......................... 79
2.2.2
The Hubert Space
............................ 80
2.2.3
Dimension and Basis of a Vector Space
................. 81
2.2.4
Square-lntegrable Functions: Wave Functions
.............. 84
2.3
Dirac Notation
.................................. 84
2.4
Operators
..................................... 89
2.4.1
General Definitions
............................ 89
2.4.2
Hermitian Adjoint
............................ 91
2.4.3
Projection Operators
........................... 92
2.4.4
Commutator Algebra
........................... 93
2.4.5
Uncertainty Relation between Two Operators
.............. 95
2.4.6
Functions of Operators
.......................... 97
2.4.7
Inverse and Unitary Operators
...................... 98
2.4.8
Eigenvalues and Eigenvectors of an Operator
.............. 99
2.4.9
Infinitesimal and Finite Unitary Transformations
............ 101
2.5
Representation in Discrete Bases
......................... 104
2.5.1
Matrix Representation of
Kets,
Bras, and Operators
........... 105
2.5.2
Change of Bases and Unitary Transformations
............. 114
2.5.3
Matrix Representation of the Eigenvalue Problem
............ 117
2.6
Representation in Continuous Bases
....................... 121
2.6.1
General Treatment
............................ 121
2.6.2
Position Representation
......................... 123
2.6.3
Momentum Representation
........................ 124
2.6.4
Connecting the Position and Momentum Representations
........ 124
2.6.5
Panty
Operator
.............................. 128
2.7
Matrix and Wave Mechanics
........................... 130
2.7.1
Matrix Mechanics
............................ 130
2.7.2
Wave Mechanics
............................. 131
2.8
Concluding Remarks
............................... 132
2.9
Solved Problems
................................. 133
2.10
Exercises
..................................... 155
3
Postulates of Quantum Mechanics
165
3.1
Introduction
.................................... 165
3.2
The Basic Postulates of Quantum Mechanics
.................. 165
3.3
The State of a System
............................... 167
3.3.1
Probability Density
............................ 167
3.3.2
The Superposition Principle
....................... 168
3.4
Observables
and Operators
............................ 170
3.5
Measurement in Quantum Mechanics
...................... 172
3.5.1
How Measurements Disturb Systems
.................. 172
3.5.2
Expectation Values
............................ 173
3.5.3
Complete Sets of Commuting Operators (CSCO)
............ 175
3.5.4
Measurement and the Uncertainty Relations
............... 177
CONTENTS
VII
3.6 Time Evolution
of the System s
State....................... 178
3.6.1
Time Evolution Operator
......................... 178
3.6.2
Stationary States: Time-Independent Potentials
............. 179
3.6.3 Schrödinger
Equation and Wave Packets
................. 180
3.6.4
The Conservation of Probability
..................... 181
3.6.5
Time Evolution of Expectation Values
.................. 182
3.7
Symmetries and Conservation Laws
....................... 183
3.7.1
Infinitesimal Unitary Transformations
.................. 184
3.7.2
Finite Unitary Transformations
...................... 185
3.7.3
Symmetries and Conservation Laws
................... 185
3.8
Connecting Quantum to Classical Mechanics
.................. 187
3.8.1
Poisson
Brackets and Commutators
................... 187
3.8.2
The
Ehrenfest
Theorem
.......................... 189
3.8.3
Quantum Mechanics and Classical Mechanics
.............. 190
3.9
Solved Problems
................................. 191
3.10
Exercises
..................................... 209
One-Dimensional Problems
215
4.1
Introduction
.................................... 215
4.2
Properties of One-Dimensional Motion
...................... 216
4.2.1
Discrete Spectrum (Bound States)
.................... 216
4.2.2
Continuous Spectrum (Unbound States)
................. 217
4.2.3
Mixed Spectrum
............................. 217
4.2.4
Symmetric Potentials and Parity
..................... 218
4.3
The Free Particle: Continuous States
....................... 218
4.4
The Potential Step
................................. 220
4.5
The Potential Barrier and Well
.......................... 224
4.5.1
The Case
E
>
Vo
............................. 224
4.5.2
The Case
E
<
y. Tunneling
...................... 227
4.5.3
The Tunneling Effect
........................... 229
4.6
The Infinite Square Well Potential
........................ 231
4.6.1
The Asymmetric Square Well
...................... 231
4.6.2
The Symmetric Potential Well
...................... 234
4.7
The Finite Square Well Potential
......................... 234
4.7.1
The Scattering Solutions (E
>
Vq)
.................... 235
4.7.2
The Bound State Solutions
(0 <
E
<
Vo)
................ 235
4.8
The Harmonic Oscillator
............................. 239
4.8.1
Energy Eigenvalues
............................ 241
4.8.2
Energy Eigenstates
............................ 243
4.8.3
Energy Eigenstates in Position Space
.................. 244
4.8.4
The Matrix Representation of Various Operators
............ 247
4.8.5
Expectation Values of Various Operators
................ 248
4.9
Numerical Solution of the
Schrödinger
Equation
................. 249
4.9.1
Numerical Procedure
........................... 249
4.9.2
Algorithm
................................. 25 1
4.10
Solved Problems
................................. 252
4.11
Exercises
..................................... 276
viii
CONTENTS
5
Angular
Momentum
283
5.1
Introduction
.................................... 283
5.2
Orbital Angular Momentum
........................... 283
5.3
General Formalism of Angular Momentum
................... 285
5.4
Matrix Representation of Angular Momentum
.................. 290
5.5
Geometrical Representation of Angular Momentum
............... 293
5.6
Spin Angular Momentum
............................. 295
5.6.1
Experimental Evidence of the Spin
.................... 295
5.6.2
General Theory of Spin
.......................... 297
5.6.3
Spin
1/2
and the
Pauli
Matrices
..................... 298
5.7
Eigenfunctions of Orbital Angular Momentum
.................. 301
5.7.1
Eigenfunctions and Eigenvalues of L:
.................. 302
5.7.2
Eigenfunctions of I2
........................... 303
5.7.3
Properties of the Spherical Harmonics
.................. 307
5.8
Solved Problems
................................. 310
5.9
Exercises
..................................... 325
6
Three-Dimensional Problems
333
6.1
Introduction
.................................... 333
6.2 3D
Problems in Cartesian Coordinates
...................... 333
6.2.1
General Treatment: Separation of Variables
............... 333
6.2.2
The Free Particle
............................. 335
6.2.3
The Box Potential
............................ 336
6.2.4
The Harmonic Oscillator
......................... 338
6.3 3D
Problems in Spherical Coordinates
...................... 340
6.3.1
Central Potential: General Treatment
.................. 340
6.3.2
The Free Particle in Spherical Coordinates
............... 343
6.3.3
The Spherical Square Well Potential
................... 346
6.3.4
The
Isotropie
Harmonic Oscillator
.................... 347
6.3.5
The Hydrogen Atom
........................... 351
6.3.6
Effect of Magnetic Fields on Central Potentials
............. 365
6.4
Concluding Remarks
............................... 368
6.5
Solved Problems
................................. 368
6.6
Exercises
..................................... 385
7
Rotations and Addition of Angular Momenta
391
7.1
Rotations in Classical Physics
.......................... 391
7.2
Rotations in Quantum Mechanics
......................... 393
7.2.1
Infinitesimal Rotations
.......................... 393
7.2.2
Finite Rotations
.............................. 395
7.2.3
Properties of the Rotation Operator
................... 396
7.2.4
Euler
Rotations
.............................. 397
7.2.5
Representation of the Rotation Operator
................. 398
7.2.6
Rotation Matrices and the Spherical Harmonics
............. 400
7.3
Addition of Angular Momenta
.......................... 403
7.3.1
Addition of Two Angular Momenta: General Formalism
........ 403
7.3.2
Calculation of the Clebsch-Gordan Coefficients
............. 409
CONTENTS ix
7.3.3
Coupling of Orbital and Spin Angular Momenta
............ 415
7.3.4
Addition of More Than Two Angular Momenta
............. 419
7.3.5
Rotation Matrices for Coupling Two Angular Momenta
......... 420
7.3.6
Isospin
.................................. 422
7.4
Scalar, Vector, and Tensor Operators
.......................425
7.4.1
Scalar Operators
............................. 426
7.4.2
Vector Operators
............................. 426
7.4.3
Tensor Operators: Reducible and Irreducible Tensors
.......... 428
7.4.4
Wigner-Eckart Theorem for Spherical Tensor Operators
........ 430
7.5
Solved Problems
................................. 434
7.6
Exercises
..................................... 450
8
Identical Particles
455
8.1
Many-Particle Systems
.............................. 455
8.1.1 Schrödinger
Equation
........................... 455
8.1.2
Interchange Symmetry
.......................... 457
8.1.3
Systems of Distinguishable Noninteracting Particles
.......... 458
8.2
Systems of Identical Particles
........................... 460
8.2.1
Identical Particles in Classical and Quantum Mechanics
........ 460
8.2.2
Exchange Degeneracy
.......................... 462
8.2.3
Symmetrization Postulate
........................ 463
8.2.4
Constructing Symmetric and Antisymmetric Functions
......... 464
8.2.5
Systems of Identical Noninteracting Particles
.............. 464
8.3
The
Pauli
Exclusion Principle
.......................... 467
8.4
The Exclusion Principle and the Periodic Table
................. 469
8.5
Solved Problems
................................. 475
8.6
Exercises
..................................... 484
9
Approximation Methods for Stationary States
489
9.1
Introduction
.................................... 489
9.2
Time-Independent Perturbation Theory
...................... 490
9.2.1
Nondegenerate
Perturbation Theory
................... 490
9.2.2
Degenerate Perturbation Theory
..................... 496
9.2.3
Fine Structure and the Anomalous
Zeeman
Effect
............ 499
9.3
The Variational Method
.............................. 507
9.4
The Wentzel-Kramers -Brillouin Method
.................... 515
9.4.1
General Formalism
............................ 515
9.4.2
Bound States for Potential Wells with No Rigid Walls
......... 518
9.4.3
Bound States for Potential Wells with One Rigid Wall
......... 524
9.4.4
Bound States for Potential Wells with Two Rigid Walls
......... 525
9.4.5
Tunneling through a Potential Barrier
.................. 528
9.5
Concluding Remarks
............................... 530
9.6
Solved Problems
................................. 531
9.7
Exercises
..................................... 562
χ
CONTENTS
10
Time-Dependent Perturbation Theory
571
10.1
Introduction
.................................... 571
10.2
The Pictures of Quantum Mechanics
....................... 571
10.2.1
The
Schrödinger
Picture
......................... 572
10.2.2
The
Heisenberg
Picture
.......................... 572
10.2.3
The Interaction Picture
.......................... 573
10.3
Time-Dependent Perturbation Theory
...................... 574
10.3.1
Transition Probability
.......................... 576
10.3.2
Transition Probability for a Constant Perturbation
............ 577
10.3.3
Transition Probability for a Harmonic Perturbation
........... 579
10.4
Adiabatic and Sudden Approximations
...................... 582
10.4.1
Adiabatic Approximation
......................... 582
10.4.2
Sudden Approximation
.......................... 583
10.5
Interaction of Atoms with Radiation
....................... 586
10.5.1
Classical Treatment of the Incident Radiation
.............. 587
10.5.2
Quantization of the Electromagnetic Field
................ 588
10.5.3
Transition Rates for Absorption and Emission of Radiation
....... 591
10.5.4
Transition Rates within the
Dipole
Approximation
........... 592
10.5.5
The Electric
Dipole
Selection Rules
................... 593
10.5.6
Spontaneous Emission
.......................... 594
10.6
Solved Problems
................................. 597
10.7
Exercises
..................................... 613
11
Scattering Theory
617
11.1
Scattering and Cross Section
........................... 617
11.1.1
Connecting the Angles in the Lab and CM frames
............ 618
11.1.2
Connecting the Lab and CM Cross Sections
............... 620
11.2
Scattering Amplitude of
Spinless
Particles
.................... 621
11.2.1
Scattering Amplitude and Differential Cross Section
.......... 623
11.2.2
Scattering Amplitude
........................... 624
11.3
The Born Approximation
............................. 628
11.3.1
The First Born Approximation
...................... 628
11.3.2
Validity of the First Born Approximation
................ 629
11.4
Partial Wave Analysis
............................... 631
11.4.1
Partial Wave Analysis for Elastic Scattering
............... 631
11.4.2
Partial Wave Analysis for Inelastic Scattering
.............. 635
11.5
Scattering of Identical Particles
.......................... 636
11.6
Solved Problems
................................. 639
11.7
Exercises
..................................... 650
A The Delta Function
653
A.I One-Dimensional Delta Function
......................... 653
A.
1.1
Various Definitions of the Delta Function
................ 653
A.
1.2
Properties of the Delta Function
..................... 654
A.
1.3
Derivative of the Delta Function
..................... 655
A.
2
Three-Dimensional Delta Function
........................ 656
CONTENTS xi
В
Angular
Momentum in Spherical Coordinates
657
B.I Derivation of Some General Relations
...................... 657
B.2 Gradient and Laplacian in Spherical Coordinates
................ 658
B.3 Angular Momentum in Spherical Coordinates
.................. 659
С
C++
Code for Solving the
Schrödinger
Equation
661
Index
665
|
| any_adam_object | 1 |
| author | Zettili, Nouredine 19XX- |
| author_GND | (DE-588)137660839 |
| author_facet | Zettili, Nouredine 19XX- |
| author_role | aut |
| author_sort | Zettili, Nouredine 19XX- |
| author_variant | n z nz |
| building | Verbundindex |
| bvnumber | BV035245888 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.12 |
| callnumber-search | QC174.12 |
| callnumber-sort | QC 3174.12 |
| callnumber-subject | QC - Physics |
| classification_rvk | UK 1000 |
| classification_tum | PHY 020f |
| ctrlnum | (OCoLC)255894625 (DE-599)BVBBV035245888 |
| dewey-full | 530.12 |
| 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 | 2nd edition |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035245888 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:29:30Z |
| institution | BVB |
| isbn | 9780470026793 9780470026786 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017051606 |
| oclc_num | 255894625 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-29T DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-83 DE-188 |
| owner_facet | DE-20 DE-703 DE-29T DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-83 DE-188 |
| physical | XVI, 671 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| spelling | Zettili, Nouredine 19XX- Verfasser (DE-588)137660839 aut Quantum mechanics concepts and applications Nouredine Zettili 2nd edition Chichester [u.a.] Wiley 2009 XVI, 671 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenmechanik (DE-588)4047989-4 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017051606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zettili, Nouredine 19XX- Quantum mechanics concepts and applications Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4123623-3 |
| title | Quantum mechanics concepts and applications |
| title_auth | Quantum mechanics concepts and applications |
| title_exact_search | Quantum mechanics concepts and applications |
| title_full | Quantum mechanics concepts and applications Nouredine Zettili |
| title_fullStr | Quantum mechanics concepts and applications Nouredine Zettili |
| title_full_unstemmed | Quantum mechanics concepts and applications Nouredine Zettili |
| title_short | Quantum mechanics |
| title_sort | quantum mechanics concepts and applications |
| title_sub | concepts and applications |
| topic | Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantentheorie Quantum theory Quantenmechanik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017051606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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