Quantum mechanics with basic field theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 838 S. |
| ISBN: | 9780521877602 |
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| 049 | |a DE-703 |a DE-20 |a DE-91G |a DE-355 | ||
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| 084 | |a UK 1000 |0 (DE-625)145785: |2 rvk | ||
| 084 | |a PHY 020f |2 stub | ||
| 100 | 1 | |a Desai, Bipin R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum mechanics with basic field theory |c Bipin R. Desai |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2010 | |
| 300 | |a XIX, 838 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Quantum theory / Problems, exercises, etc | |
| 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 |
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| adam_text | Preface
page
xvii
Physical constants
XX
1
Basic
formalism
1
1.1
State vectors
1
1.2
Operators and physical
observables
3
1.3
Eigenstates
4
1.4
Hermitian conjugation and Hermitian operators
5
1.5
Hermitian operators: their eigenstates and eigenvalues
6
1.6
Superposition principle
7
1.7
Completeness relation
8
1.8
Unitary operators
9
1.9
Unitary operators as transformation operators
10
1.10
Matrix formalism
12
1.11
Eigenstates and diagonalization of matrices
16
1.12
Density operator
18
1.13
Measurement
20
1.14
Problems
21
2
Fundamental commutator and time evolution of state vectors
and operators
24
2.1
Continuous variables: X and
Ρ
operators
24
2.2
Canonical commutator [X, P]
26
2.3
Ρ
as a derivative operator: another way
29
2.4
X and
Ρ
as Hermitian operators
30
2.5
Uncertainty principle
32
2.6
Some interesting applications of uncertainty relations
35
2.7
Space displacement operator
36
2.8
Time evolution operator
41
2.9
Appendix to Chapter
2
44
2.10
Problems
52
3
Dynamical equations
55
3.1
Schrödinger
picture
55
Heisenberg
oicture
57
v¡¡¡
Contents
3.3
Interaction
picture
59
3.4
Superposition
of time-dependent states and energy-time
uncertainty relation
63
3.5
Time dependence of the density operator
66
3.6
Probability conservation
67
3.7
Ehrenfest s theorem
68
3.8
Problems
70
4
Free particles
73
4.1
Free particle in one dimension
73
4.2
Normalization
75
4.3
Momentum eigenfimctions and Fourier transforms
78
4.4
Minimum uncertainty wave packet
79
4.5
Group velocity of a superposition of plane waves
83
4.6
Three dimensions
-
Cartesian coordinates
84
4.7
Three dimensions
-
spherical coordinates
87
4.8
The radial wave equation
91
4.9
Properties of
Y¡m{9,
φ)
92
4.10
Angular momentum
94
4.11
Determining
Ĺ2
from the angular variables
97
4.12
Commutator
[L¡, L¡
and
[L2,
Lj
98
4.13
Ladder operators
100
4.14
Problems
102
5
Particles with spin V2
103
5.1
Spin V2 system
103
5.2 Pauli
matrices
104
5.3
The spin V2 eigenstates
105
5.4
Matrix representation of
σχ
and ay
106
5.5
Eigenstates of
σχ
and ay
108
5.6
Eigenstates of spin in an arbitrary direction
109
5.7
Some important relations for
σ,
110
5.8
Arbitrary
2x2
matrices in terms of
Pauli
matrices
111
5.9
Projection operator for spin XA systems
112
5.10
Density matrix for spin
Vi
states and the ensemble average
114
5.11
Complete wavefimction
116
5.12 Pauli
exclusion principle and Fermi energy
116
5.13
Problems
118
6
Gauge
invariance,
angular momentum, and spin
120
6.1
Gauge
invariance
120
6.2
Quantum mechanics
121
6.3
Canonical and kinematic momenta
123
6.4
Probability conservation
124
ix Contents
6.5
Interaction
with the
orbital
angular
momentom
125
6.6
Interaction with spin: intrinsic magnetic moment
126
6.7
Spin—orbit interaction
128
6.8
Aharonov-Bohm effect
129
6.9
Problems
131
7
Stern-Gerlach experiments
133
7.1
Experimental set-up and electron s magnetic moment
133
7.2
Discussion of the results
134
7.3
Problems
136
8
Some exactly solvable bound-state problems
137
8.1
Simple one-dimensional systems
137
8.2
Delta-function potential
145
8.3
Properties of a symmetric potential
147
8.4
The ammonia molecule
148
8.5
Periodic potentials
151
8.6
Problems in three dimensions
156
8.7
Simple systems
160
8.8
Hydrogen-like atom
164
8.9
Problems
170
9
Harmonic oscillator
174
9.1
Harmonic oscillator in one dimension
174
9.2
Problems
184
10
Coherent states
187
10.1
Eigenstates of the lowering operator
187
10.2
Coherent states and semiclassical description
192
10.3
Interaction of a harmonic oscillator with an electric field
194
10.4
Appendix to Chapter
10 199
10.5
Problems
200
11
Two-dimensional
isotropie
harmonic oscillator
203
11.1
The two-dimensional Hamiltonian
203
11.2
Problems
207
12
Landau levels and quantum Hall effect
208
12.1
Landau levels in symmetric gauge
208
12.2
Wavefunctions for the LLL
212
12.3
Landau levels in Landau gauge
214
12.4
Quantum Hall effect
216
12.5
Wavefimction for filled LLLs in a Fermi system
220
12.6
Problems
221
Contents
13
Two-level problems 223
13.1
Time-independent problems 223
13.2
Time-dependent problems 234
13.3
Problems 246
14
Spin 1/2 systems in the presence of magnetic fields
251
14.1
Constant magnetic field 25
1
14.2
Spin precession 2^4
14.3
Time-dependent magnetic field: spin magnetic resonance
255
14.4
Problems 258
15
Oscillation and regeneration in neutrinos and neutral K-mesons
as two-level systems
260
15.1
Neutrinos
260
15.2
The solar neutrino puzzle
260
15.3
Neutrino oscillations
263
15.4
Decay and regeneration
265
15.5
Oscillation and regeneration of stable and unstable systems
269
15.6
Neutral /¿ -mesons
273
15.7
Problems
276
16
Time-independent perturbation for bound states
277
16.1
Basic formalism
277
16.2
Harmonic oscillator: perturbative vs. exact results
281
16.3
Second-order Stark effect
284
16.4
Degenerate states
287
16.5
Linear Stark effect
289
16.6
Problems
290
17
Time-dependent perturbation
293
17.1
Basic formalism
293
17.2
Harmonic perturbation and Fermi s golden rule
296
17.3
Transitions into a group of states and scattering cross-section
299
17.4
Resonance and decay
303
17.5
Appendix to Chapter
17 310
17.6
Problems 315
18
Interaction of charged particles and radiation in perturbation theory
318
18.1
Electron in an electromagnetic field: the absorption cross-section
318
18.2
Photoelectric effect
323
18.3
Coulomb excitations of an atom
325
18.4
Ionization 32g
18.5
Thomson, Rayleigh, and Raman scattering in second-order
perturbation
33
j
18.6
Problems
339
xi Contents
19
Scattering in one
dimension
342
19.1
Reflection and
transmission coefficients
342
19.2
Infinite barrier
344
19.3
Finite barrier with infinite range
345
19.4
Rigid wall preceded by a potential well
348
19.5
Square-well potential and resonances
351
19.6
Tunneling
354
19.7
Problems
356
20
Scattering in three dimensions
-
a formal theory
358
20.1
Formal solutions in terms of Green s function
358
20.2
Lippmann-Schwinger equation
360
20.3
Born approximation
363
20.4
Scattering from a Yukawa potential
364
20.5
Rutherford scattering
365
20.6
Charge distribution
366
20.7
Probability conservation and the optical theorem
367
20.8
Absorption
370
20.9
Relation between the
Г
-matrix
and the scattering amplitude
372
20.10
The S-matrix
374
20.11
Unitarity of the S-matrix and the relation between
S
and
Τ
378
20.12
Properties of the
Г
-matrix
and the optical theorem (again)
382
20.13
Appendix to Chapter
20 383
20.14
Problems
384
21
Partial wave amplitudes and phase shifts
386
21.1
Scattering amplitude in terms of phase shifts
386
21.2
χ,,Κ,,ζηάΤ,
392
21.3
Integral relations for
χ,,ΑΓ/,
and
Γ/
393
21.4
Wronskian
395
21.5
Calculation of phase shifts: some examples
400
21.6
Problems
405
22
Analytic structure of the S-matrix
407
22.1
S-matrix poles
407
22.2
Jost function formalism
413
22.3
Levinson
s
theorem
420
22.4
Explicit calculation of the Jost function for/
= 0 421
22.5
Integral representation of Fo(k)
424
22.6
Problems
426
23
Poles of the Green s function and composite systems
427
23.1
Relation between the time-evolution operator and the
Green s function
427
23.2
Stable and unstable states
429
xü
Contents
23.3
Scattering amplitude and resonance
430
23.4
Complex poles
431
23.5
Two types of resonances
431
23.6
The reaction matrix
432
23.7
Composite systems
442
23.8
Appendix to Chapter
23 447
24
Approximation methods for bound states and scattering
450
24.1
WKB approximation
450
24.2
Variational method
458
24.3
Eikonal approximation
461
24.4
Problems
466
25
Lagrangian method and Feynman path integrals
469
25.1
Euler-Lagrange equations
469
25.2 N
oscillators and the continuum limit
471
25.3
Feynman path integrals
473
25.4
Problems
478
26
Rotations and angular momentum
479
26.1
Rotation of coordinate axes
479
26.2
Scalar functions and orbital angular momentum
483
26.3
State vectors
485
26.4
Transformation of matrix elements and representations of the
rotation operator
487
26.5
Generators of infinitesimal rotations: their eigenstates
and eigenvalues
489
26.6
Representations of J2 and J,
fory
=
andy
= 1 494
26.7
Spherical harmonics
495
26.8
Problems
501
27
Symmetry in quantum mechanics and symmetry groups
502
27.1
Rotational symmetry
502
27.2
Parity transformation
505
27.3
Time reversal 507
27.4
Symmetry groups
5
j
27.5
D> (R)
fory
=
andy
= 1 :
examples of S0(3) and SU(2) groups
514
27.6
Problems 5J5
28
Addition of angular momenta
5
¡
g
28.1
Combining eigenstates: simple examples
5
j g
28.2
Clebsch-Gordan coefficients and their recursion relations
522
28.3
Combining spin V2 and orbital angular momentum
/ 524
28.4
Appendix to Chapter
28 527
28.5
Problems
xiii Contents
29
Irreducible tensors and Wigner-Eckart theorem
529
29.1
Irreducible spherical tensors and their properties
529
29.2
The irreducible tensors: Ylm
(θ, φ)
and D>
(χ
) 533
29.3
Wigner-Eckart theorem
536
29.4
Applications of the Wigner-Eckart theorem
538
29.5
Appendix to Chapter
29:
SO(3), SU(2) groups and Young s tableau
541
29.6
Problems
548
30
Entangled states
549
30.1
Definition of an entangled state
549
30.2
The singlet state
551
30.3
Differentiating the two approaches
552
30.4
Bell s inequality
553
30.5
Problems
555
31
Special theory of relativity: Klein-Gordon and Maxwell s equations
556
31.1
Lorentz
transformation
556
31.2
Contravariant
and covariant vectors
557
31.3
An example of a covariant vector
560
31.4
Generalization to arbitrary tensors
561
31.5
Relativistically invariant equations
563
31.6
Appendix to Chapter
31 569
31.7
Problems
572
32
Klein-Gordon and Maxwell s equations
575
32.1
Covariant equations in quantum mechanics
575
32.2
Klein-Gordon equations: free particles
576
32.3
Normalization of matrix elements
578
32.4
Maxwell s equations
579
32.5
Propagators
581
32.6
Virtual particles
586
32.7
Static approximation
586
32.8
Interaction potential in nonrelativistic processes
587
32.9
Scattering interpreted as an exchange of virtual particles
589
32.10
Appendix to Chapter
32 593
33
The Dirac equation
597
33.1
Basic formalism
597
33.2
Standard representation and spinor solutions
600
33.3
Large and small components of u(p)
601
33.4
Probability conservation
605
33.5
Spin
Vi
for the Dirac particle
607
34
Dirac equation in the presence of spherically symmetric potentials
611
34.1
Spin-orbit coupling
611
Xjv
Contents
34.2
Jí-operator
for the spherically symmetric potentials
613
34.3
Hydrogen atom 616
34.4
Radial Dirac equation
618
34.5
Hydrogen atom states
623
34.6
Hydrogen atom wavefunction
624
34.7
Appendix to Chapter
34 626
35
Dirac equation in a relativistically invariant form
631
35.1
Covariant Dirac equation
631
35.2
Properties of the y-matrices
632
35.3
Charge-current conservation in a covariant form
633
35.4
Spinor solutions: ur(p) and vr(p)
635
35.5
Normalization and completeness condition for ur(p) and vr(p)
636
35.6
Gordon decomposition
640
35.7
Lorentz
transformation of the Dirac equation
642
35.8
Appendix to Chapter
35 644
36
Interaction of a Oirac particle with an electromagnetic field
647
36.1
Charged particle Hamiltonian
647
36.2
Deriving the equation another way
650
36.3
Gordon decomposition and electromagnetic current
651
36.4
Dirac equation with EM field and comparison with the
Klein-Gordon equation
653
36.5
Propagators: the Dirac propagator
655
36.6
Scattering
657
36.7
Appendix to Chapter
36 661
37
Multiparticle systems and second quantization
663
37.1
Wavefunctions for identical particles
663
37.2
Occupation number space and ladder operators
664
37.3
Creation and destruction operators
666
37.4
Writing single-particle relations in multiparticle language: the
operators, N, H, and
Ρ
670
37.5
Matrix elements of a potential
67
1
37.6
Free fields and continuous variables
672
37.7
Klein-Gordon/scalar field
674
37.8
Complex scalar field
678
37.9
Dirac field
680
37.10
Maxwell field 683
37.11
Lorentz covariance
for Maxwell field
687
37.12
Propagators and time-ordered products
688
37.13
Canonical quantization q^q
37.14 Casimir
effect 693
37.15
Problems
xv Contents
38
Interactions
of electrons and phonons in condensed matter
699
38.1
Fermi energy
699
38.2
Interacting electron gas
704
38.3
Phonons
708
38.4
Electron—phonon interaction
713
39
Superconductivity
719
39.1
Many-body system of half-integer spins
719
39.2
Normal states
(Δ
= 0,
G
φ
0) 724
39.3
BCS states
(Δ φ
0) 725
39.4
BCS condensate in Green s function formalism
727
39.5
Meissner effect
732
39.6
Problems
735
40
Bose-Einstein condensation and superfluidity
736
40.1
Many-body system of integer spins
736
40.2
Superfluidity
740
40.3
Problems
742
41
Lagrangian formulation of classical fields
743
41.1
Basic structure
743
41.2
Noether s theorem
744
41.3
Examples
746
41.4
Maxwell s equations and consequences of gauge
invariance
750
42
Spontaneous symmetry breaking
755
42.1
BCS mechanism
755
42.2
Ferromagnetism
756
42.3
SSB for discrete symmetry in classical field theory
758
42.4
SSB for continuous symmetry
760
42.5
Nambu-Goldstone bosons
762
42.6
Higgs mechanism
765
43
Basic quantum electrodynamics and Feynman diagrams
770
43.1
Perturbation theory
770
43.2
Feynman diagrams
773
43.3
Τ
(H¡
(x
)
Hi (x2)) and Wick s theorem
777
43.4
Feynman rules
783
43.5
Cross-section for
1 + 2 -»3 + 4 783
43.6
Basic two-body scattering in QED
786
43.7
QED vs. nonrelativistic limit: electron-electron system
786
43.8
QED vs. nonrelativistic limit: electron-photon system
789
44
Radiative corrections
793
44.1
Radiative corrections and renormalization
793
xvi Contents
44.2 Electron
self-energy
794
44.3 Appendix
to Chapter
44 799
45
Anomalous magnetic moment and Lamb shift
806
45.1
Calculating the divergent integrals
806
45.2
Vertex function and the magnetic moment
806
45.3
Calculation of the vertex function diagram
808
45.4
Divergent part of the vertex function
810
45.5
Radiative corrections to the photon propagator
811
45.6
Divergent part of the photon propagator
813
45.7
Modification of the photon propagator and photon wavefunction
814
45.8
Combination of all the divergent terms: basic renormalization
816
45.9
Convergent parts of the radiative corrections
817
45.10
Appendix to Chapter
45 821
Bibliography
825
Index
828
|
| any_adam_object | 1 |
| author | Desai, Bipin R. |
| author_facet | Desai, Bipin R. |
| author_role | aut |
| author_sort | Desai, Bipin R. |
| author_variant | b r d br brd |
| building | Verbundindex |
| bvnumber | BV035773543 |
| 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)434562740 (DE-599)BVBBV035773543 |
| 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 | 1. publ. |
| format | Book |
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| id | DE-604.BV035773543 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:04:13Z |
| institution | BVB |
| isbn | 9780521877602 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018633187 |
| oclc_num | 434562740 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-91G DE-BY-TUM DE-355 DE-BY-UBR |
| owner_facet | DE-703 DE-20 DE-91G DE-BY-TUM DE-355 DE-BY-UBR |
| physical | XIX, 838 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Desai, Bipin R. Verfasser aut Quantum mechanics with basic field theory Bipin R. Desai 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2010 XIX, 838 S. txt rdacontent n rdamedia nc rdacarrier Quantum theory Quantum theory / Problems, exercises, etc Quantentheorie Quantum theory Problems, exercises, etc Quantenmechanik (DE-588)4047989-4 gnd rswk-swf 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=018633187&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Desai, Bipin R. Quantum mechanics with basic field theory Quantum theory Quantum theory / Problems, exercises, etc Quantentheorie Quantum theory Problems, exercises, etc Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 |
| title | Quantum mechanics with basic field theory |
| title_auth | Quantum mechanics with basic field theory |
| title_exact_search | Quantum mechanics with basic field theory |
| title_full | Quantum mechanics with basic field theory Bipin R. Desai |
| title_fullStr | Quantum mechanics with basic field theory Bipin R. Desai |
| title_full_unstemmed | Quantum mechanics with basic field theory Bipin R. Desai |
| title_short | Quantum mechanics with basic field theory |
| title_sort | quantum mechanics with basic field theory |
| topic | Quantum theory Quantum theory / Problems, exercises, etc Quantentheorie Quantum theory Problems, exercises, etc Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantum theory Quantum theory / Problems, exercises, etc Quantentheorie Quantum theory Problems, exercises, etc Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018633187&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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