Quantum mechanics: a new introduction
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| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2009
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 778 S. Ill., graph. Darst. 1 CD-ROM (12 cm), 1 Beibl. |
| ISBN: | 9780199560271 9780199560264 |
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| 020 | |a 9780199560271 |9 978-0-19-956027-1 | ||
| 020 | |a 9780199560264 |9 978-0-19-956026-4 | ||
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| 084 | |a UK 1000 |0 (DE-625)145785: |2 rvk | ||
| 084 | |a PHY 020f |2 stub | ||
| 100 | 1 | |a Konishi, Kenichi |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum mechanics |b a new introduction |c Kenichi Konishi and Giampiero Paffuti |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2009 | |
| 300 | |a XIX, 778 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm), 1 Beibl. | ||
| 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 | 4 | |a Quantum theory |v Problems, exercises, etc | |
| 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 Paffuti, Giampiero |e Verfasser |0 (DE-588)137830955 |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=016670569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| adam_text | Contents
I
Basic
quantum mechanics
1
Introduction
5
1.1
The quantum behavior of the electron
5
1.1.1
Diffraction and interference
—
visualizing the quan¬
tum world
5
1.1.2
The stability and identity of atoms
6
1.1.3
Tunnel effects
8
1.2
The birth of quantum mechanics
9
1.2.1
Erom.
the theory of specific heat to Planck s formula
9
1.2.2
The photoelectric effect
14
1.2.3
Bohr s atomic model
15
1.2.4
The Bohr-Sommerfeld quantization condition;
de
Brogue s wave
17
Further reading
18
Guide to the Supplements
18
Problems
19
Numerical analyses
19
2
Quantum mechanical laws
21
2.1
Quantum states
21
2.1.1
Composite systems
24
2.1.2
Photon polarization and the statistical nature of
quantum mechanics
24
2.2
The uncertainty principle
26
2.3
The fundamental postulate
29
2.3.1
The projection operator and state vector reduction
31
2.3.2
Hermitian operators
32
2.3.3
Products of operators, commutators, and compat¬
ible
observables
33
2.3.4
The position operator, the momentum operator,
fundamental commutators, and Heisenberg s rela¬
tion
35
2.3.5
Heisenberg s relations
36
2.4
The
Schrödinger
equation
37
2.4.1
More about the
Schrödinger
equations
38
2.4.2
The
Heisenberg
picture
40
2.5
The continuous spectrum
40
2.5.1
The delta function
41
2.5.2
Orthogonality
43
χ
Contents
2.5.3
The position and momentum eigenstates; momen¬
tum as a translation operator
43
2.6
Completeness
45
Problems
47
Numerical analyses
48
The
Schrödinger
equation
49
3.1
General properties
49
3.1.1
Boundary conditions
49
3.1.2
Ehrenfest s theorem
50
3.1.3
Current density and conservation of probability
51
3.1.4
The virial and Feynman-Hellman theorems
52
3.2
One-dimensional systems
53
3.2.1
The free particle
54
3.2.2
Topologically
nontrivial
space
55
3.2.3
Special properties of one-dimensional
Schrödinger
equations
56
3.3
Potential wells
58
3.3.1
Infinitely deep wells (walls)
58
3.3.2
The finite square well
59
3.3.3
An application
61
3.4
The harmonic oscillator
63
3.4.1
The wave function and Hermite polynomials
63
3.4.2
Creation and annihilation operators
67
3.5
Scattering problems and the tunnel effect
71
3.5.1
The potential barrier and the tunnel effect
71
3.5.2
The delta function potential
74
3.5.3
General aspects of the scattering problem
78
3.6
Periodic potentials
80
3.6.1
The band structure of the energy spectrum
80
3.6.2
Analysis
82
Guide to the Supplements
84
Problems
85
Numerical analyses
87
Angular momentum
89
4.1
Commutation relations
89
4.2
Space rotations
91
4.3
Quantization
92
4.4
The Stern-Gerlach experiment
95
4.5
Spherical harmonics
96
4.6
Matrix elements of
J
98
4.6.1
Spin-ì
and
Pauli
matrices
100
4.7
The composition rule
101
4.7.1
The Clebsch-Gordan coefficients
104
4-8
Spin
105
4.8.1
Rotation matrices for spin ~
107
Guide to the Supplements
108
Contents xi
Problems 109
5
Symmetry and statistics 111
5.1
Symmetries in Nature 111
5.2
Symmetries in quantum mechanics
113
5.2.1
The ground state and symmetry
116
5.2.2
Parity (V)
117
5.2.3
Time reversal
121
5.2.4
The Galilean transformation
123
5.2.5
The Wigner-Eckart theorem
125
5.3
Identical particles: Bose-Einstein and Fermi-Dirac statis¬
tics
127
5.3.1
Identical bosons
130
5.3.2
Identical
fermions
and Pauli s exclusion principle
132
Guide to the Supplements
133
Problems
134
6
Three-dimensional problems
135
6.1
Simple three-dimensional systems
135
6.1.1
Reduced mass
135
6.1.2
Motion in a spherically symmetric potential
136
6.1.3
Spherical waves
137
6.2
Bound states in potential wells
140
6.3
The three-dimensional oscillator
141
6.4
The hydrogen atom
143
Guide to the Supplements
148
Problems
149
Numerical analyses
150
7
Some finer points of quantum mechanics
151
7.1
Representations
151
7.1.1
Coordinate and momentum representations
152
7.2
States and operators
155
7.2.1
Bra and
ket;
abstract Hilbert space
155
7.3
Unbounded operators
158
7.3.1
Self-adjoint operators
160
7.4
Unitary transformations
167
7.5
The
Heisenberg
picture
169
7.5.1
The harmonic oscillator in the
Heisenberg
picture
171
7.6
The uncertainty principle
172
7.7
Mixed states and the density matrix
173
7.7.1
Photon polarization
176
7.8
Quantization in general coordinates
178
Further reading
182
Guide to the Supplements
182
Problems
182
8
Path integrals
183
8.1
Green functions
183
xii Contents
8.2
Path integrals
186
8.2.1
Derivation
186
8.2.2
Mode expansion
190
8.2.3
Feynman graphs
192
8.2.4
Back to ordinary (Minkowski) time
197
8.2.5
Tunnel effects and
instantons
198
Further reading
201
Numerical analyses
202
II Approximation methods
203
9
Perturbation theory
207
9.1
Time-independent perturbations
207
9.1.1
Degenerate levels
212
9.1.2
The Stark effect on the
η
= 2
level of the hydrogen
atom
214
9.1.3 Dipole
interactions and polarizability
217
9.2
Quantum transitions
219
9.2.1
Perturbation lasting for a finite interval
221
9.2.2
Periodic perturbation
223
9.2.3
Transitions in a discrete spectrum
223
9.2.4
Resonant oscillation between two levels
225
9.3
Transitions in the continuum
226
9.3.1
State density
228
9.4
Decays
228
9.5
Electromagnetic transitions
233
9.5.1
The
dipole
approximation
234
9.5.2
Absorption of radiation
237
9.5.3
Induced (or stimulated) emission
238
9.5.4
Spontaneous emission
239
9.6
The Einstein coefficients
240
Guide to the Supplements
242
Problems
242
Numerical analyses
244
10
Variational methods
245
10.1
The variational principle
245
10.1.1
Lower limits
247
10.1.2
Truncated Hubert space
249
10.2
Simple applications
250
10.2.1
The harmonic oscillator
250
10.2.2
Helium: an elementary variational calculation
252
10.2.3
The viriai theorem
254
10.3
The ground state of the helium
255
Guide to the Supplements
261
Problems
261
Numerical analyses
262
Contents xiii
11
The semi-classical approximation
265
11.1
The WKB approximation
265
11.1.1
Connection formulas
268
11.2
The Bohr-Sommerfeld quantization condition
271
11.2.1
Counting the quantum states
273
11.2.2
Potentials defined for
χ
> 0
only
275
11.2.3
On the meaning of the limit
ћ
-*· 0 276
11.2.4
Angular variables
276
11.2.5
Radial equations
279
11.2.6
Examples
282
11.3
The tunnel effect
283
11.3.1
The double well
285
11.3.2
The semi-classical treatment of decay processes
289
11.3.3
The Gamow-Siegert theory
292
11.4
Phase shift
295
Further reading
300
Guide to the Supplements
300
Problems
301
Numerical analyses
302
III Applications
303
12
Time evolution
307
12.1
General features of time evolution
307
12.2
Time-dependent unitary transformations
309
12.3
Adiabatic processes
311
12.3.1
The Landau-Zener transition
313
12.3.2
The impulse approximation
315
12.3.3
The Berry phase
316
12.3.4
Examples
318
12.4
Some
nontrivial
systems
320
12.4.1
A particle within moving walls
320
12.4.2
Resonant oscillations
324
12.4.3
A particle encircling a solenoid
327
12.4.4
A ring with a defect
328
12.5
The cyclic harmonic oscillator: a theorem
331
12.5.1
Inverse linear variation of the frequency
335
12.5.2
The Planck distribution inside an oscillating cavity
336
12.5.3
General power-dependent frequencies
338
12.5.4
Exponential dependence
339
12.5.5
Creation and annihilation operators; coupled os¬
cillators
340
Guide to the Supplements
341
Problems
341
Numerical analyses
342
13
Metastable states
343
xiv Contents
13.1 Green
functions
343
13.1.1
Analytic properties of the resolvent
345
13.1.2
Free particles
349
13.1.3
The free Green function in general dimensions
351
13.1.4
Expansion in powers of Hi
352
13.2
Metastable states
356
13.2.1
Formulation of the problem
356
13.2.2
The width of a metastable state; the mean half-
lifetime
358
13.2.3
Formal treatment
361
13.3
Examples
368
13.3.1
Discrete-continuum coupling
368
13.4
Complex scale transformations
370
13.4.1
Analytic continuation
372
13.5
Applications and examples
374
13.5.1
Resonances in helium
375
13.5.2
The potential Vo r2e~r
375
13.5.3
The unbounded potential; the
Lo
Surdo-Stark effect376
Further reading
379
Problems
379
Numerical analyses
379
14
Electromagnetic interactions
381
14.1
The charged particle in an electromagnetic field
381
14.1.1
Classical particles
381
14.1.2
Quantum particles in electromagnetic fields
383
14.1.3 Dipole
and quadrupole interactions
385
14.1.4
Magnetic interactions
388
14.1.5
Relativistic corrections: LS coupling
388
14.1.6
Hyperfine interactions
390
14.2
The Aharonov-Bohm effect
392
14.2.1
Superconductors
395
14.3
The Landau levels
397
14.3.1
The quantum Hall effect
399
14.4
Magnetic
monopoles
401
Guide to the Supplements
404
Problems
404
Numerical analyses
404
15
Atoms
405
15.1
Electronic configurations
405
15.1.1
The ionization potential
408
15.1.2
The spectrum of alkali metals
410
15.1.3
Xrays
410
15.2
The
Hartree
approximation
412
15.2.1
Self-consistent fields and the variational principle
415
15.2.2
Some results
417
15.3
Multiplets
418
Contents xv
15.3.1
Structure
of the
multiplets
419
15.4
Slater determinants
424
15.5
The Hartree-Fock approximation
427
15.5.1
Examples
430
15.6
Spin-orbit interactions
433
15.6.1
The hydrogen atom
436
15.7
Atoms in external electric fields
438
15.7.1 Dipole
interaction and polarizability
438
15.7.2
Quadrupole interactions
442
15.8
The
Zeeman
effect
443
15.8.1
The
Zeeman
effect in quantum mechanics
444
Further reading
450
Guide to the Supplements
451
Problems
451
Numerical analyses
452
16
Elastic scattering theory
453
16.1
The cross section
453
16.2
Partial wave expansion
457
16.2.1
The semi-classical limit
459
16.3
The Lippman-Schwinger equation
460
16.4
The Born approximation
461
16.5
The eikonal approximation
463
16.6
Low-energy scattering
465
16.7
Coulomb scattering: Rutherford s formula
468
16.7.1
Scattering of identical particles
473
Further reading
474
Guide to the Supplements
475
Problems
476
Numerical analyses
476
17
Atomic nuclei and elementary particles
477
17.1
Atomic nuclei
477
17.1.1
General features
477
17.1.2
Isospin
478
17.1.3
Nuclear forces,
pion
exchange, and the Yukawa
potential
480
17.1.4
Radioactivity
482
17.1.5
The
deuteron
and two-nucleon forces
483
17.2
Elementary particles: the need for relativistic quantum
field theories
485
17.2.1
The Klein-Gordon and Dirac equations
487
17.2.2
Quantization of the free Klein-Gordon fields
490
17.2.3
Quantization of the free Dirac fields and the spin-
statistics connection
491
17.2.4
Causality and locality
492
17.2.5
Self-interacting scalar fields
494
17.2.6
Non-Abelian gauge theories: the Standard Model
495
xvi Contents
Further reading
496
IV Entanglement and Measurement
499
18
Quantum entanglement
503
18.1
The EPRB
Gedankenexperiment
and quantum entangle¬
ment
503
18.2
Aspect s experiment
508
18.3
Entanglement with more than two particles
511
18.4
Factorization versus entanglement
512
18.5
A measure of entanglement: entropy
514
Further reading
516
19
Probability and measurement
517
19.1
The probabilistic nature of quantum mechanics
517
19.2
Measurement and state preparation: from PVM to POVM519
19.3
Measurement problems
521
19.3.1
The EPR paradox
522
19.3.2
Measurement as a physical process: decoherence
and the classical limit
525
19.3.3 Schrödinger s
cat
527
19.3.4
The fundamental postulate versus
Schrödinger s
equation
529
19.3.5
Is quantum mechanics exact?
530
19.3.6
Cosmology and quantum mechanics
531
19.4
Hidden-variable theories
532
19.4.1
Bell s inequalities
532
19.4.2
The Kochen-Specker theorem
535
19.4.3
Quantum non-locality versus locally causal the¬
ories or local realism
538
Further reading
539
Guide to the Supplements
539
V Supplements
541
20
Supplements for Part I
545
20.1
Classical mechanics
545
20.1.1
The Lagrangian formalism
545
20.1.2
The Hamiltonian (canonical) formalism
547
20.1.3
Poisson
brackets
549
20.1.4
Canonical transformations
550
20.1.5
The Hamilton-Jacobi equation
552
20.1.6
Adiabatic invariants
552
20.1.7
The virial theorem
554
20.2
The Hamiltonian of electromagnetic radiation field in the
vacuum
554
Contents xvii
20.3
Orthogonality and completeness in a system with a one-
dimensional delta function potential
556
20.3.1
Orthogonality
557
20.3.2
Completeness
558
20.4
The
S
matrix; the wave packet description of scattering
560
20.4.1
The wave packet description
560
20.5
Legendre polynomials
564
20.6
Groups and representations
566
20.6.1
Group axioms; some examples
566
20.6.2
Group representations
568
20.6.3
Lie groups and Lie algebras
570
20.6.4
The U(N) group and the quarks
573
20.7
Formulas for angular momentum
575
20.8
Young tableaux
581
20.9
TV-particle matrix elements
584
20.10
The Fock representation
586
20.10.1
Bosons
586
20.10.2
Fermions
588
20.11
Second quantization
589
20.12
Supersymmetry in quantum mechanics
590
20.13
Two- and three-dimensional delta function potentials
595
20.13.1
Bound states
597
20.13.2
Self-adjoint extensions
598
20.13.3
The two-dimensional delta-function potential: a
quantum anomaly
599
20.14
Superselection rules
601
20.15
Quantum representations
604
20.15.1
Weyl s commutation relations
605
20.15.2 Von
Neumann s theorem
605
20.15.3
Angular variables
606
20.15.4
Canonical transformations
608
20.15.5
Self-adjoint extensions
610
20.16
Gaussian integrals and Feynman graphs
611
21
Supplements for Part II
615
21.1
Supplements on perturbation theory
615
21.1.1
Change of boundary conditions
615
21.1.2
Two-level systems
616
21.1.3
Van
der Waals
interactions
618
21.1.4
The Dalgarno-Lewis method
619
21.2
The fine structure of the hydrogen atom
621
21.2.1
A semi-classical model for the Lamb shift
626
21.3
Hydrogen hyperfine interactions
630
21.4
Divergences of perturbative series
633
21.4.1
Perturbative series at large orders: the anharmonic
oscillator
633
21.4.2
The origin of the divergence
635
21.4.3
The analyticity domain
636
xviii Contents
21
A A Asymptotic series
638
21.4.5
The dispersion relation
642
21.4.6
The perturbative-variational approach
645
21.5
The semi-classical approximation in general systems
648
21.5.1
Introduction
648
21.5.2
Keller quantization
650
21.5.3
Integrable
systems
653
21.5.4
Examples
654
21.5.5
Caustics
655
21.5.6
The
KAM
theorem and quantization
655
22
Supplementsjor Part III
657
22.1
The K°-K° system and CP violation
657
22.2
Level density
661
22.2.1
The free particle
665
22.2.2
g(E) and the partition function
666
22.2.3
g(E) and short-distance behavior
669
22.2.4
Level density and scattering
671
22.2.5
The stabilization method
673
22.3
Thomas precession
674
22.4
Relativistic corrections in an external field
676
22.5
The Hamiltonian for interacting charged particles
678
22.5.1
The interaction potentials
679
22.5.2
Spin-dependent interactions
681
22.5.3
The quantum Hamiltonian
682
22.5.4
Electron-electron interactions
682
22.5.5
Electron-nucleus interactions
683
22.5.6
The 1/M corrections
686
22.6
Quantization of electromagnetic fields
687
22.6.1
Matrix elements
689
22.7
Atoms
692
22.7.1
The Thomas-Fermi approximation
693
22.7.2
The
Hartree
approximation
700
22.7.3
Slater determinants and matrix elements
703
22.7.4
Hamiltonians for closed shells
707
22.7.5
Mean energy
712
22.7.6
Hamiltonians for incomplete shells
712
22.7.7
Eigenvalues of
Я
716
22.7.8
The elementary theory of
multiplets
717
22.7.9
The Hartree-Fock equations
719
22.7.10The role of
Lagrange
multipliers
721
22.7.11
Koopman s theorem
723
22.8
H}
726
22.9
The Gross-Pitaevski equation
729
22.10
The semi-classical scattering amplitude
731
22.10.1
Caustics and rainbows
732
23
Supplements for Part IV
735
Contents xix
23.1 Speakable
and unspeakable in quantum mechanics
735
23.1.1
Bell s toy model for hidden variables
735
23.1.2
Bohm s pilot waves
736
23.1.3
The many-worlds interpretation
739
23.1.4
Spontaneous wave function collapse
740
24
Mathematical appendices and tables
743
24.1
Mathematical appendices
743
24.1.1
Laplace s method
743
24.1.2
The saddle-point method
744
24.1.3
Airy functions
748
References
765
Index
775
|
| adam_txt |
Contents
I
Basic
quantum mechanics
1
Introduction
5
1.1
The quantum behavior of the electron
5
1.1.1
Diffraction and interference
—
visualizing the quan¬
tum world
5
1.1.2
The stability and identity of atoms
6
1.1.3
Tunnel effects
8
1.2
The birth of quantum mechanics
9
1.2.1
Erom.
the theory of specific heat to Planck's formula
9
1.2.2
The photoelectric effect
14
1.2.3
Bohr's atomic model
15
1.2.4
The Bohr-Sommerfeld quantization condition;
de
Brogue's wave
17
Further reading
18
Guide to the Supplements
18
Problems
19
Numerical analyses
19
2
Quantum mechanical laws
21
2.1
Quantum states
21
2.1.1
Composite systems
24
2.1.2
Photon polarization and the statistical nature of
quantum mechanics
24
2.2
The uncertainty principle
26
2.3
The fundamental postulate
29
2.3.1
The projection operator and state vector reduction
31
2.3.2
Hermitian operators
32
2.3.3
Products of operators, commutators, and compat¬
ible
observables
33
2.3.4
The position operator, the momentum operator,
fundamental commutators, and Heisenberg's rela¬
tion
35
2.3.5
Heisenberg's relations
36
2.4
The
Schrödinger
equation
37
2.4.1
More about the
Schrödinger
equations
38
2.4.2
The
Heisenberg
picture
40
2.5
The continuous spectrum
40
2.5.1
The delta function
41
2.5.2
Orthogonality
43
χ
Contents
2.5.3
The position and momentum eigenstates; momen¬
tum as a translation operator
43
2.6
Completeness
45
Problems
47
Numerical analyses
48
The
Schrödinger
equation
49
3.1
General properties
49
3.1.1
Boundary conditions
49
3.1.2
Ehrenfest's theorem
50
3.1.3
Current density and conservation of probability
51
3.1.4
The virial and Feynman-Hellman theorems
52
3.2
One-dimensional systems
53
3.2.1
The free particle
54
3.2.2
Topologically
nontrivial
space
55
3.2.3
Special properties of one-dimensional
Schrödinger
equations
56
3.3
Potential wells
58
3.3.1
Infinitely deep wells (walls)
58
3.3.2
The finite square well
59
3.3.3
An application
61
3.4
The harmonic oscillator
63
3.4.1
The wave function and Hermite polynomials
63
3.4.2
Creation and annihilation operators
67
3.5
Scattering problems and the tunnel effect
71
3.5.1
The potential barrier and the tunnel effect
71
3.5.2
The delta function potential
74
3.5.3
General aspects of the scattering problem
78
3.6
Periodic potentials
80
3.6.1
The band structure of the energy spectrum
80
3.6.2
Analysis
82
Guide to the Supplements
84
Problems
85
Numerical analyses
87
Angular momentum
89
4.1
Commutation relations
89
4.2
Space rotations
91
4.3
Quantization
92
4.4
The Stern-Gerlach experiment
95
4.5
Spherical harmonics
96
4.6
Matrix elements of
J
98
4.6.1
Spin-ì
and
Pauli
matrices
100
4.7
The composition rule
101
4.7.1
The Clebsch-Gordan coefficients
104
4-8
Spin
105
4.8.1
Rotation matrices for spin ~
107
Guide to the Supplements
108
Contents xi
Problems 109
5
Symmetry and statistics 111
5.1
Symmetries in Nature 111
5.2
Symmetries in quantum mechanics
113
5.2.1
The ground state and symmetry
116
5.2.2
Parity (V)
117
5.2.3
Time reversal
121
5.2.4
The Galilean transformation
123
5.2.5
The Wigner-Eckart theorem
125
5.3
Identical particles: Bose-Einstein and Fermi-Dirac statis¬
tics
127
5.3.1
Identical bosons
130
5.3.2
Identical
fermions
and Pauli's exclusion principle
132
Guide to the Supplements
133
Problems
134
6
Three-dimensional problems
135
6.1
Simple three-dimensional systems
135
6.1.1
Reduced mass
135
6.1.2
Motion in a spherically symmetric potential
136
6.1.3
Spherical waves
137
6.2
Bound states in potential wells
140
6.3
The three-dimensional oscillator
141
6.4
The hydrogen atom
143
Guide to the Supplements
148
Problems
149
Numerical analyses
150
7
Some finer points of quantum mechanics
151
7.1
Representations
151
7.1.1
Coordinate and momentum representations
152
7.2
States and operators
155
7.2.1
Bra and
ket;
abstract Hilbert space
155
7.3
Unbounded operators
158
7.3.1
Self-adjoint operators
160
7.4
Unitary transformations
167
7.5
The
Heisenberg
picture
169
7.5.1
The harmonic oscillator in the
Heisenberg
picture
171
7.6
The uncertainty principle
172
7.7
Mixed states and the density matrix
173
7.7.1
Photon polarization
176
7.8
Quantization in general coordinates
178
Further reading
182
Guide to the Supplements
182
Problems
182
8
Path integrals
183
8.1
Green functions
183
xii Contents
8.2
Path integrals
186
8.2.1
Derivation
186
8.2.2
Mode expansion
190
8.2.3
Feynman graphs
192
8.2.4
Back to ordinary (Minkowski) time
197
8.2.5
Tunnel effects and
instantons
198
Further reading
201
Numerical analyses
202
II Approximation methods
203
9
Perturbation theory
207
9.1
Time-independent perturbations
207
9.1.1
Degenerate levels
212
9.1.2
The Stark effect on the
η
= 2
level of the hydrogen
atom
214
9.1.3 Dipole
interactions and polarizability
217
9.2
Quantum transitions
219
9.2.1
Perturbation lasting for a finite interval
221
9.2.2
Periodic perturbation
223
9.2.3
Transitions in a discrete spectrum
223
9.2.4
Resonant oscillation between two levels
225
9.3
Transitions in the continuum
226
9.3.1
State density
228
9.4
Decays
228
9.5
Electromagnetic transitions
233
9.5.1
The
dipole
approximation
234
9.5.2
Absorption of radiation
237
9.5.3
Induced (or stimulated) emission
238
9.5.4
Spontaneous emission
239
9.6
The Einstein coefficients
240
Guide to the Supplements
242
Problems
242
Numerical analyses
244
10
Variational methods
245
10.1
The variational principle
245
10.1.1
Lower limits
247
10.1.2
Truncated Hubert space
249
10.2
Simple applications
250
10.2.1
The harmonic oscillator
250
10.2.2
Helium: an elementary variational calculation
252
10.2.3
The viriai theorem
254
10.3
The ground state of the helium
255
Guide to the Supplements
261
Problems
261
Numerical analyses
262
Contents xiii
11
The semi-classical approximation
265
11.1
The WKB approximation
265
11.1.1
Connection formulas
268
11.2
The Bohr-Sommerfeld quantization condition
271
11.2.1
Counting the quantum states
273
11.2.2
Potentials defined for
χ
> 0
only
275
11.2.3
On the meaning of the limit
ћ
-*· 0 276
11.2.4
Angular variables
276
11.2.5
Radial equations
279
11.2.6
Examples
282
11.3
The tunnel effect
283
11.3.1
The double well
285
11.3.2
The semi-classical treatment of decay processes
289
11.3.3
The Gamow-Siegert theory
292
11.4
Phase shift
295
Further reading
300
Guide to the Supplements
300
Problems
301
Numerical analyses
302
III Applications
303
12
Time evolution
307
12.1
General features of time evolution
307
12.2
Time-dependent unitary transformations
309
12.3
Adiabatic processes
311
12.3.1
The Landau-Zener transition
313
12.3.2
The impulse approximation
315
12.3.3
The Berry phase
316
12.3.4
Examples
318
12.4
Some
nontrivial
systems
320
12.4.1
A particle within moving walls
320
12.4.2
Resonant oscillations
324
12.4.3
A particle encircling a solenoid
327
12.4.4
A ring with a defect
328
12.5
The cyclic harmonic oscillator: a theorem
331
12.5.1
Inverse linear variation of the frequency
335
12.5.2
The Planck distribution inside an oscillating cavity
336
12.5.3
General power-dependent frequencies
338
12.5.4
Exponential dependence
339
12.5.5
Creation and annihilation operators; coupled os¬
cillators
340
Guide to the Supplements
341
Problems
341
Numerical analyses
342
13
Metastable states
343
xiv Contents
13.1 Green
functions
343
13.1.1
Analytic properties of the resolvent
345
13.1.2
Free particles
349
13.1.3
The free Green function in general dimensions
351
13.1.4
Expansion in powers of Hi
352
13.2
Metastable states
356
13.2.1
Formulation of the problem
356
13.2.2
The width of a metastable state; the mean half-
lifetime
358
13.2.3
Formal treatment
361
13.3
Examples
368
13.3.1
Discrete-continuum coupling
368
13.4
Complex scale transformations
370
13.4.1
Analytic continuation
372
13.5
Applications and examples
374
13.5.1
Resonances in helium
375
13.5.2
The potential Vo r2e~r
375
13.5.3
The unbounded potential; the
Lo
Surdo-Stark effect376
Further reading
379
Problems
379
Numerical analyses
379
14
Electromagnetic interactions
381
14.1
The charged particle in an electromagnetic field
381
14.1.1
Classical particles
381
14.1.2
Quantum particles in electromagnetic fields
383
14.1.3 Dipole
and quadrupole interactions
385
14.1.4
Magnetic interactions
388
14.1.5
Relativistic corrections: LS coupling
388
14.1.6
Hyperfine interactions
390
14.2
The Aharonov-Bohm effect
392
14.2.1
Superconductors
395
14.3
The Landau levels
397
14.3.1
The quantum Hall effect
399
14.4
Magnetic
monopoles
401
Guide to the Supplements
404
Problems
404
Numerical analyses
404
15
Atoms
405
15.1
Electronic configurations
405
15.1.1
The ionization potential
408
15.1.2
The spectrum of alkali metals
410
15.1.3
Xrays
410
15.2
The
Hartree
approximation
412
15.2.1
Self-consistent fields and the variational principle
415
15.2.2
Some results
417
15.3
Multiplets
418
Contents xv
15.3.1
Structure
of the
multiplets
419
15.4
Slater determinants
424
15.5
The Hartree-Fock approximation
427
15.5.1
Examples
430
15.6
Spin-orbit interactions
433
15.6.1
The hydrogen atom
436
15.7
Atoms in external electric fields
438
15.7.1 Dipole
interaction and polarizability
438
15.7.2
Quadrupole interactions
442
15.8
The
Zeeman
effect
443
15.8.1
The
Zeeman
effect in quantum mechanics
444
Further reading
450
Guide to the Supplements
451
Problems
451
Numerical analyses
452
16
Elastic scattering theory
453
16.1
The cross section
453
16.2
Partial wave expansion
457
16.2.1
The semi-classical limit
459
16.3
The Lippman-Schwinger equation
460
16.4
The Born approximation
461
16.5
The eikonal approximation
463
16.6
Low-energy scattering
465
16.7
Coulomb scattering: Rutherford's formula
468
16.7.1
Scattering of identical particles
473
Further reading
474
Guide to the Supplements
475
Problems
476
Numerical analyses
476
17
Atomic nuclei and elementary particles
477
17.1
Atomic nuclei
477
17.1.1
General features
477
17.1.2
Isospin
478
17.1.3
Nuclear forces,
pion
exchange, and the Yukawa
potential
480
17.1.4
Radioactivity
482
17.1.5
The
deuteron
and two-nucleon forces
483
17.2
Elementary particles: the need for relativistic quantum
field theories
485
17.2.1
The Klein-Gordon and Dirac equations
487
17.2.2
Quantization of the free Klein-Gordon fields
490
17.2.3
Quantization of the free Dirac fields and the spin-
statistics connection
491
17.2.4
Causality and locality
492
17.2.5
Self-interacting scalar fields
494
17.2.6
Non-Abelian gauge theories: the Standard Model
495
xvi Contents
Further reading
496
IV Entanglement and Measurement
499
18
Quantum entanglement
503
18.1
The EPRB
Gedankenexperiment
and quantum entangle¬
ment
503
18.2
Aspect's experiment
508
18.3
Entanglement with more than two particles
511
18.4
Factorization versus entanglement
512
18.5
A measure of entanglement: entropy
514
Further reading
516
19
Probability and measurement
517
19.1
The probabilistic nature of quantum mechanics
517
19.2
Measurement and state preparation: from PVM to POVM519
19.3
Measurement "problems"
521
19.3.1
The EPR "paradox"
522
19.3.2
Measurement as a physical process: decoherence
and the classical limit
525
19.3.3 Schrödinger's
cat
527
19.3.4
The fundamental postulate versus
Schrödinger's
equation
529
19.3.5
Is quantum mechanics exact?
530
19.3.6
Cosmology and quantum mechanics
531
19.4
Hidden-variable theories
532
19.4.1
Bell's inequalities
532
19.4.2
The Kochen-Specker theorem
535
19.4.3
"Quantum non-locality" versus "locally causal the¬
ories" or "local realism"
538
Further reading
539
Guide to the Supplements
539
V Supplements
541
20
Supplements for Part I
545
20.1
Classical mechanics
545
20.1.1
The Lagrangian formalism
545
20.1.2
The Hamiltonian (canonical) formalism
547
20.1.3
Poisson
brackets
549
20.1.4
Canonical transformations
550
20.1.5
The Hamilton-Jacobi equation
552
20.1.6
Adiabatic invariants
552
20.1.7
The virial theorem
554
20.2
The Hamiltonian of electromagnetic radiation field in the
vacuum
554
Contents xvii
20.3
Orthogonality and completeness in a system with a one-
dimensional delta function potential
556
20.3.1
Orthogonality
557
20.3.2
Completeness
558
20.4
The
S
matrix; the wave packet description of scattering
560
20.4.1
The wave packet description
560
20.5
Legendre polynomials
564
20.6
Groups and representations
566
20.6.1
Group axioms; some examples
566
20.6.2
Group representations
568
20.6.3
Lie groups and Lie algebras
570
20.6.4
The U(N) group and the quarks
573
20.7
Formulas for angular momentum
575
20.8
Young tableaux
581
20.9
TV-particle matrix elements
584
20.10
The Fock representation
586
20.10.1
Bosons
586
20.10.2
Fermions
588
20.11
Second quantization
589
20.12
Supersymmetry in quantum mechanics
590
20.13
Two- and three-dimensional delta function potentials
595
20.13.1
Bound states
597
20.13.2
Self-adjoint extensions
598
20.13.3
The two-dimensional delta-function potential: a
quantum anomaly
599
20.14
Superselection rules
601
20.15
Quantum representations
604
20.15.1
Weyl's commutation relations
605
20.15.2 Von
Neumann's theorem
605
20.15.3
Angular variables
606
20.15.4
Canonical transformations
608
20.15.5
Self-adjoint extensions
610
20.16
Gaussian integrals and Feynman graphs
611
21
Supplements for Part II
615
21.1
Supplements on perturbation theory
615
21.1.1
Change of boundary conditions
615
21.1.2
Two-level systems
616
21.1.3
Van
der Waals
interactions
618
21.1.4
The Dalgarno-Lewis method
619
21.2
The fine structure of the hydrogen atom
621
21.2.1
A semi-classical model for the Lamb shift
626
21.3
Hydrogen hyperfine interactions
630
21.4
Divergences of perturbative series
633
21.4.1
Perturbative series at large orders: the anharmonic
oscillator
633
21.4.2
The origin of the divergence
635
21.4.3
The analyticity domain
636
xviii Contents
21
A A Asymptotic series
638
21.4.5
The dispersion relation
642
21.4.6
The perturbative-variational approach
645
21.5
The semi-classical approximation in general systems
648
21.5.1
Introduction
648
21.5.2
Keller quantization
650
21.5.3
Integrable
systems
653
21.5.4
Examples
654
21.5.5
Caustics
655
21.5.6
The
KAM
theorem and quantization
655
22
Supplementsjor Part III
657
22.1
The K°-K° system and CP violation
657
22.2
Level density
661
22.2.1
The free particle
665
22.2.2
g(E) and the partition function
666
22.2.3
g(E) and short-distance behavior
669
22.2.4
Level density and scattering
671
22.2.5
The stabilization method
673
22.3
Thomas precession
674
22.4
Relativistic corrections in an external field
676
22.5
The Hamiltonian for interacting charged particles
678
22.5.1
The interaction potentials
679
22.5.2
Spin-dependent interactions
681
22.5.3
The quantum Hamiltonian
682
22.5.4
Electron-electron interactions
682
22.5.5
Electron-nucleus interactions
683
22.5.6
The 1/M corrections
686
22.6
Quantization of electromagnetic fields
687
22.6.1
Matrix elements
689
22.7
Atoms
692
22.7.1
The Thomas-Fermi approximation
693
22.7.2
The
Hartree
approximation
700
22.7.3
Slater determinants and matrix elements
703
22.7.4
Hamiltonians for closed shells
707
22.7.5
Mean energy
712
22.7.6
Hamiltonians for incomplete shells
712
22.7.7
Eigenvalues of
Я
716
22.7.8
The elementary theory of
multiplets
717
22.7.9
The Hartree-Fock equations
719
22.7.10The role of
Lagrange
multipliers
721
22.7.11
Koopman's theorem
723
22.8
H}
726
22.9
The Gross-Pitaevski equation
729
22.10
The semi-classical scattering amplitude
731
22.10.1
Caustics and rainbows
732
23
Supplements for Part IV
735
Contents xix
23.1 Speakable
and unspeakable in quantum mechanics
735
23.1.1
Bell's toy model for hidden variables
735
23.1.2
Bohm's pilot waves
736
23.1.3
The many-worlds interpretation
739
23.1.4
Spontaneous wave function collapse
740
24
Mathematical appendices and tables
743
24.1
Mathematical appendices
743
24.1.1
Laplace's method
743
24.1.2
The saddle-point method
744
24.1.3
Airy functions
748
References
765
Index
775 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Konishi, Kenichi Paffuti, Giampiero |
| author_GND | (DE-588)137830955 |
| author_facet | Konishi, Kenichi Paffuti, Giampiero |
| author_role | aut aut |
| author_sort | Konishi, Kenichi |
| author_variant | k k kk g p gp |
| building | Verbundindex |
| bvnumber | BV035001172 |
| 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)234430697 (DE-599)BVBBV035001172 |
| 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 |
| discipline_str_mv | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035001172 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:40:33Z |
| indexdate | 2024-07-09T21:19:55Z |
| institution | BVB |
| isbn | 9780199560271 9780199560264 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016670569 |
| oclc_num | 234430697 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-20 DE-29T DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-20 DE-29T DE-11 DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| physical | XIX, 778 S. Ill., graph. Darst. 1 CD-ROM (12 cm), 1 Beibl. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Konishi, Kenichi Verfasser aut Quantum mechanics a new introduction Kenichi Konishi and Giampiero Paffuti 1. publ. Oxford [u.a.] Oxford Univ. Press 2009 XIX, 778 S. Ill., graph. Darst. 1 CD-ROM (12 cm), 1 Beibl. txt rdacontent n rdamedia nc rdacarrier Quantentheorie Quantum theory Quantum theory Problems, exercises, etc Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Paffuti, Giampiero Verfasser (DE-588)137830955 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016670569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Konishi, Kenichi Paffuti, Giampiero Quantum mechanics a new introduction Quantentheorie Quantum theory Quantum theory Problems, exercises, etc Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 |
| title | Quantum mechanics a new introduction |
| title_auth | Quantum mechanics a new introduction |
| title_exact_search | Quantum mechanics a new introduction |
| title_exact_search_txtP | Quantum mechanics a new introduction |
| title_full | Quantum mechanics a new introduction Kenichi Konishi and Giampiero Paffuti |
| title_fullStr | Quantum mechanics a new introduction Kenichi Konishi and Giampiero Paffuti |
| title_full_unstemmed | Quantum mechanics a new introduction Kenichi Konishi and Giampiero Paffuti |
| title_short | Quantum mechanics |
| title_sort | quantum mechanics a new introduction |
| title_sub | a new introduction |
| topic | Quantentheorie Quantum theory Quantum theory Problems, exercises, etc Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantentheorie Quantum theory Quantum theory Problems, exercises, etc Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016670569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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