Quantum mechanics: with ... 16 tables, numerous worked examples and 127 problems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Edition: | 4. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 424 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783540719328 3540719326 |
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MARC
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| 245 | 1 | 0 | |a Quantum mechanics |b with ... 16 tables, numerous worked examples and 127 problems |c Franz Schwabl |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XV, 424 S. |b Ill., graph. Darst. |c 24 cm | ||
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| _version_ | 1804137442548121600 |
|---|---|
| adam_text | FRANZ SCHWABL
QUANTU
M MECHANICS
FOURTH EDITION
WITH 123 FIGURES, 16 TABLES,
NUMEROUS WORKED EXAMPLES AND 127 PROBLEMS
YJ.
SPRINGER
TABLE OF CONTENTS
1. HISTORICA
L
AN
D
EXPERIMENTA
L
FOUNDATION
S
1
1.1 INTRODUCTION AND OVERVIEW 1
1.2 HISTORICALLY FUNDAMENTAL EXPERIMENTS AND INSIGHTS 3
1.2.1 PARTICLE PROPERTIES OF ELECTROMAGNETIC WAVES 3
1.2.2 WAVE PROPERTIES OF PARTICLES,
DIFFRACTION OF MATTE
R WAVES 7
1.2.3 DISCRETE STATES 8
2. TH
E WAVE FUNCTIO
N AN
D TH
E SCHRODINGE
R EQUATIO
N
13
2.1 THE WAVE FUNCTION AND ITS PROBABILITY INTERPRETATION 13
2.2 THE SCHRODINGER EQUATION FOR FREE PARTICLES 15
2.3 SUPERPOSITION OF PLANE WAVES 16
2.4 THE PROBABILITY DISTRIBUTION FOR A MEASUREMENT
OF MOMENTUM 19
2.4.1 ILLUSTRATION OF TH
E UNCERTAINTY PRINCIPLE 21
2.4.2 MOMENTUM IN-COORDINATE SPACE 22
2.4.3 OPERATORS AND THE SCALAR PRODUC
T 23
2.5 THE CORRESPONDENCE PRINCIPLE AND TH
E SCHRODINGER EQUATION 26
2.5.1 THE CORRESPONDENCE PRINCIPLE 26
2.5.2 THE POSTULATES OF QUANTUM THEORY 27
2.5.3 MANY-PARTICLE SYSTEMS 28
2.6 THE EHRENFEST THEOREM 28
2.7 THE CONTINUITY EQUATION FOR TH
E PROBABILITY DENSITY 31
2.8 STATIONARY SOLUTIONS OF THE SCHRODINGER EQUATION,
EIGENVALUE EQUATIONS 32
2.8.1 STATIONARY STATES 32
2.8.2 EIGENVALUE EQUATIONS . 33
2.8.3 EXPANSION IN STATIONARY STATES 35
2.9 THE PHYSICAL SIGNIFICANCE OF TH
E EIGENVALUES OF AN OPERATOR 36
2.9.1 SOME CONCEPTS FROM PROBABILITY THEORY 36
2.9.2 APPLICATION T
O OPERATORS WITH DISCRETE EIGENVALUES 37
2.9.3 APPLICATION T
O OPERATORS
WITH A CONTINUOUS SPECTRUM 38
2.9.4 AXIOMS OF QUANTUM THEORY 40
X TABLE OF CONTENTS
2.10 ADDITIONAL POINTS 41
2.10.1 THE GENERAL WAVE PACKET 41
2.10.2 REMARK ON TH
E NORMALIZABILITY
OF TH
E CONTINUUM STATES 43
PROBLEMS 44
3
. ONE-DIMENSIONA
L PROBLEM
S
47
3.1 THE HARMONIC OSCILLATOR T 47
3.1.1 THE ALGEBRAIC METHOD 48
3.1.2 THE HERMITE POLYNOMIALS 52
3.1.3 TH
E ZERO-POINT ENERGY 54
3.1.4 COHERENT STATES 56
3.2 POTENTIAL STEPS 58
3.2.1 CONTINUITY OF
IP(X)
AND
TJJ {X)
FOR A PIECEWISE CONTINUOUS POTENTIAL 58
3.2.2 TH
E POTENTIAL STEP 59
3.3 TH
E TUNNELING EFFECT, TH
E POTENTIA
L BARRIER 64
3.3.1 THE POTENTIAL BARRIER 64
3.3.2 TH
E CONTINUOUS POTENTIAL BARRIER 67
3.3.3 EXAMPLE OF APPLICATION: A-DECAY 68
3.4 THE POTENTIAL WELL 71
3.4.1 EVEN SYMMETRY 72
3.4.2 ODD SYMMETRY 73
3.5 SYMMETRY PROPERTIES 76
3.5.1 PARIT
Y 76
3.5.2 CONJUGATION 77
3.6 GENERAL DISCUSSION
OF TH
E ONE-DIMENSIONAL SCHRODINGER EQUATION 77
3.7 THE POTENTIAL WELL, RESONANCES 81
3.7.1 ANALYTIC PROPERTIES OF TH
E TRANSMISSION COEFFICIENT. 83
3.7.2 THE MOTION OF A WAVE PACKET NEAR A RESONANCE ..
. 87
PROBLEMS , 92
4
. TH
E UNCERTAINT
Y RELATIO
N
97
4.1 TH
E HEISENBERG UNCERTAINTY RELATION 97
4.1.1 THE SCHWARZ INEQUALITY 97
4.1.2 THE GENERAL UNCERTAINTY RELATION 97
4.2 ENERGY-TIME UNCERTAINTY 99
4.2.1 PASSAGE TIME AND ENERGY UNCERTAINTY 100
4.2.2 DURATION OF AN ENERGY MEASUREMENT
AND ENERGY UNCERTAINTY 100
4.2.3 LIFETIME AND ENERGY UNCERTAINTY 101
4.3 COMMON EIGENFUNCTIONS OF COMMUTING OPERATORS 102
PROBLEMS . . . .
106
TABLE OF CONTENTS XI
5. ANGULAR MOMENTU
M
107
5.1 COMMUTATION RELATIONS, ROTATIONS 107
5.2 EIGENVALUES OF ANGULAR MOMENTUM OPERATORS . .-. 110
5.3 ORBITAL ANGULAR MOMENTUM IN POLAR COORDINATES 112
PROBLEMS 118
6. THE CENTRAL POTENTIA
L I
119
6.1 SPHERICAL COORDINATES 119
6.2 BOUND STATES IN THREE DIMENSIONS 122
6.3 THE COULOMB POTENTIAL 124
6.4 THE TWO-BODY PROBLEM 138
PROBLEMS 140
7. MOTIO
N IN A
N ELECTROMAGNETI
C FIEL
D
.
V
143
7.1 THE HAMILTONIAN 143
7.2 CONSTANT MAGNETIC FIELD
B
144
7.3 THE NORMAL ZEEMAN EFFECT 145
7.4 CANONICAL AND KINETIC MOMENTUM, GAUGE TRANSFORMATION.. 147
7.4.1 CANONICAL AND KINETIC MOMENTUM 147
7.4.2 CHANGE OF THE WAVE FUNCTION
UNDER A GAUGE TRANSFORMATION 148
7.5 THE AHARONOV-BOHM EFFECT 149
7.5.1 THE WAVE FUNCTION IN A REGION
FREE OF MAGNETIC FIELDS 149
7.5.2 THE AHARONOV-BOHM INTERFERENCE EXPERIMENT 150
7.6 FLUX QUANTIZATION IN SUPERCONDUCTORS 153
7.7 FREE ELECTRONS IN A MAGNETIC FIELD 154
PROBLEMS 155
8. OPERATORS, MATRICES
, STAT
E VECTOR
S
159
8.1 MATRICES, VECTORS, AND UNITARY TRANSFORMATIONS 159
8.2 STATE VECTORS AND DIRAC NOTATION 164
8.3 THE AXIOMS OF QUANTUM MECHANICS 169
8.3.1 COORDINATE REPRESENTATION 170
8.3.2 MOMENTUM REPRESENTATION 171
8.3.3 REPRESENTATION IN TERMS OF A DISCRETE BASIS SYSTEM 172
8.4 MULTIDIMENSIONAL SYSTEMS S,
AND MANY-PARTICLE SYSTEMS 172
8.5 THE SCHRODINGER, HEISENBERG
AND INTERACTION REPRESENTATIONS 173
8.5.1 THE SCHRODINGER REPRESENTATION 173
8.5.2 THE HEISENBERG REPRESENTATION 174
8.5.3 THE INTERACTION PICTURE (OR DIRAC REPRESENTATION) . 176
8.6 THE MOTION OF A FREE ELECTRON IN A MAGNETIC FIELD 177
PROBLEMS 181
XII TABLE OF CONTENTS
9. SPIN
183
9.1 THE EXPERIMENTAL DISCOVERY
OF THE INTERNAL ANGULAR MOMENTUM 183
9.1.1 THE NORMAL ZEEMAN EFFECT 183
9.1.2 THE STERN-GERLACH EXPERIMENT 183
9.2 MATHEMATICAL FORMULATION FOR SPIN-1/2 185
9.3 PROPERTIES OF THE PAULI MATRICES ^ 186
9.4 STATES, SPINORS 187
9.5 MAGNETIC MOMENT 188
9.6 SPATIAL DEGREES OF FREEDOM AND SPIN 189
PROBLEMS 191
10. ADDITIO
N OF ANGULAR MOMENT
A
193
10.1 POSING THE PROBLEM 193
10.2 ADDITION OF SPIN-1/2 OPERATORS 194
10.3 ORBITAL ANGULAR MOMENTUM AND SPIN 1/2 196
10.4 THE GENERAL CASE 198
PROBLEMS 201
11
. APPROXIMATIO
N METHOD
S FOR STATIONAR
Y STATE
S
203
11.1 TIME INDEPENDENT PERTURBATION THEORY
(RAYLEIGH-SCHRODINGER) 203
11.1.1 NONDEGENERATE PERTURBATION THEORY 204
11.1.2 PERTURBATION THEORY FOR DEGENERATE STATES 206
11.2 THE VARIATIONAL PRINCIPLE 207
11.3 THE WKB (WENTZEL-KRAMERS-BRILLOUIN) METHOD 208
11.4 BRILLOUIN-WIGNER PERTURBATION THEORY 211
PROBLEMS
(
212
12
.
RELATIVISTI
C CORRECTION
S
215
12.1 RELATIVISTIC KINETIC ENERGY . .
. 215
12.2 SPIN-ORBIT COUPLING 217
12.3 THE DARWIN TERM 219
12.4 FURTHER CORRECTIONS 222
12.4.1 THE LAMB SHIFT 222
12.4.2 HYPERFINE STRUCTURE 222
PROBLEMS
* 225
13
.
SEVERAL-ELECTRO
N ATOM
S
227
13.1 IDENTICAL PARTICLES 227
13.1.1 BOSONS AND FERMIONS 227
13.1.2 NONINTERACTING PARTICLES 230
13.2 HELIUM .
/
. 233
13.2.1 WITHOUT THE ELECTRON-ELECTRON INTERACTION 233
TABLE OF CONTENTS XIII
13.2.2 ENERGY SHIFT
DUE T
O THE REPULSIVE ELECTRON-ELECTRON INTERACTION 235
13.2.3 THE VARIATIONAL METHOD : 240
13.3 THE HARTREE AND HARTREE-FOCK APPROXIMATIONS
(SELF-CONSISTENT FIELDS) 241
13.3.1 THE HARTREE APPROXIMATION 242
13.3.2 THE HARTREE-FOCK APPROXIMATION 244
13.4 THE THOMAS-FERMI METHOD . . .
247
13.5 ATOMIC STRUCTURE AND HUND S RULES 252
PROBLEMS 258
14. TH
E ZEEMA
N EFFECT AN
D TH
E STARK EFFECT
259
14.1 THE HYDROGEN ATOM IN A MAGNETIC FIELD 259
14.1.1 WEAK FIELD 260
14.1.2 STRONG FIELD, THE PASCHEN-BACK EFFECT 260
14.1.3 THE ZEEMAN EFFECT FOR AN ARBITRARY MAGNETIC FIELD 261
14.2 MULTIELECTRON ATOMS 264
14.2.1 WEAK MAGNETIC FIELD 264
14.2.2 STRONG MAGNETIC FIELD, THE PASCHEN-BACK EFFECT . . . 266
14.3 THE STARK EFFECT 266
14.3.1 ENERGY SHIFT OF THE GROUND STAT
E 267
14.3.2 EXCITED STATES 267
PROBLEMS 269
15. MOLECULE
S
271
15.1 QUALITATIVE CONSIDERATIONS 271
15.2 THE BORN-OPPENHEIMER APPROXIMATION 273
15.3 THE HYDROGEN MOLECULAR ION (H^) 275
15.4 THE HYDROGEN MOLECULE H
2
278
15.5 ENERGY LEVELS OF A TWO-ATOM MOLECULE:
VIBRATIONAL AND ROTATIONAL LEVELS 282
15.6 THE VAN DER WAALS FORCE 284
PROBLEMS 287
16. TIM
E DEPENDEN
T PHENOMEN
A
289
16.1 THE HEISENBERG PICTUR
E FOR A TIME DEPENDENT HAMILTONIAN. 289
16.2 THE SUDDEN APPROXIMATION T 291
16.3 TIME DEPENDENT PERTURBATIO
N THEORY 292
16.3.1 PERTURBATIVE EXPANSION , 292
16.3.2 FIRST-ORDER TRANSITIONS 294
16.3.3 TRANSITIONS INTO A CONTINUOUS SPECTRUM,
THE GOLDEN RULE 294
16.3.4 PERIODIC PERTURBATION
S 297
16.4 INTERACTION WITH THE RADIATION FIELD 298
16.4.1 THE HAMILTONIAN 298
XIV TABLE OF CONTENTS
16.4.2 QUANTIZATION OF THE RADIATION FIELD 299
16.4.3 SPONTANEOUS EMISSION 301
16.4.4 ELECTRIC DIPOLE
(EL)
TRANSITIONS 303
16.4.5 SELECTION RULES FOR ELECTRIC DIPOLE
(EL)
TRANSITIONS 303
16.4.6 THE LIFETIME FOR ELECTRIC DIPOLE TRANSITIONS 306
16.4.7 ELECTRIC QUADRUPOLE
AND MAGNETIC DIPOLE TRANSITIONS 307
16.4.8 ABSORPTION AND INDUCED EMISSION 309
PROBLEMS : 310
17. TH
E CENTRAL POTENTIA
L II
313
17.1 THE SCHRODINGER EQUATION
FOR A SPHERICALLY SYMMETRIC SQUARE WELL 313
17.2 SPHERICAL BESSEL FUNCTIONS 314
17.3 BOUND STATES OF TH
E SPHERICAL POTENTIAL WELL 316
17.4 THE LIMITING CASE OF A DEEP POTENTIAL WELL 318
17.5 CONTINUUM SOLUTIONS FOR THE POTENTIAL WELL 320
17.6 EXPANSION OF PLANE WAVES IN SPHERICAL HARMONICS 321
PROBLEMS 324
18. SCATTERIN
G THEOR
Y
325
18.1 SCATTERING OF A WAVE PACKET AND STATIONARY STATES 325
18.1.1 THE WAVE PACKET 325
18.1.2 FORMAL SOLUTION
OF THE TIME INDEPENDENT SCHRODINGER EQUATION ...
. 326
18.1.3 ASYMPTOTIC BEHAVIOR OF THE WAVE PACKET 328
18.2 THE SCATTERING CROSS SECTION 330
18.3 PARTIAL WAVES , 331
18.4 THE OPTICAL THEOREM . 335
18.5 THE BORN APPROXIMATION 337
18.6 INELASTIC SCATTERING 339
18.7 SCATTERING PHASE SHIFTS 340
18.8 RESONANCE SCATTERING FROM A POTENTIAL WELL 342
18.9 LOW ENERGY S-WAVE SCATTERING; THE SCATTERING LENGTH 346
18.10 SCATTERING A
T HIGH ENERGIES 349
18.11 ADDITIONAL REMARKS 351
18.11.1 TRANSFORMATION TO THE LABORATORY FRAME 351
18.11.2 THE COULOMB POTENTIAL 352
PROBLEMS 352
19. SUPERSYMMETRI
C QUANTU
M THEOR
Y
355
19.1 GENERALIZED LADDER OPERATORS 355
19.2 EXAMPLES. 358
19.2.1 REFLECTION-FREE POTENTIALS 358
19.2.2 THE (5-FUNCTION 361
TABLE OF CONTENTS XV
19.2.3 THE HARMONIC OSCILLATOR 361
19.2.4 THE COULOMB POTENTIAL 362
19.3 ADDITIONAL REMARKS 365
PROBLEMS 367
20. STAT
E AND MEASUREMEN
T I
N QUANTU
M MECHANIC
S
369
20.
1
THE QUANTUM MECHANICAL STATE, CAUSALITY,
AND DETERMINISM .- 369
20.2 THE DENSITY MATRIX 371
20.2.1 THE DENSITY MATRIX FOR PURE AND MIXED ENSEMBLES 371
20.2.2 THE VON NEUMANN EQUATION 376
20.2.3 SPIN-1/2 SYSTEMS 377
20.3 THE MEASUREMENT PROCESS 380
20.3.1 THE STERN-GERLACH EXPERIMENT 380
20.3.2 THE QUASICLASSICAL SOLUTION 381
20.3.3 THE STERN-GERLACH EXPERIMENT
AS AN IDEALIZED MEASUREMENT : 381
20.3.4 A GENERAL EXPERIMENT
AND COUPLING T
O TH
E ENVIRONMENT 383
20.3.5 INFLUENCE OF AN OBSERVATION ON THE TIME EVOLUTION . 387
20.3.6 PHASE RELATIONS IN TH
E STERN-GERLACH EXPERIMENT. . 389
20.4 THE EPR ARGUMENT, HIDDEN VARIABLES, THE BELL INEQUALITY . 390
20.4.1 THE EP
R (EINSTEIN-PODOLSKY-ROSEN) ARGUMENT ..
. 390
20.4.2 THE BELL INEQUALITY 392
PROBLEMS 396
APPENDI
X
399
A. MATHEMATICAL TOOLS FOR THE SOLUTION
OF LINEAR DIFFERENTIAL EQUATIONS 399
A.I THE FOURIER TRANSFORM 399
A.2 THE DELTA FUNCTION AND DISTRIBUTIONS 399
A.3 GREEN S FUNCTIONS 404
B. CANONICAL AND KINETIC MOMENTUM 405
C. ALGEBRAIC DETERMINATION
OF THE ORBITAL ANGULAR MOMENTUM EIGENFUNCTIONS 406
D. THE PERIODIC TABLE AND IMPORTANT PHYSICAL QUANTITIES 412
SUBJECT INDEX
417
|
| adam_txt |
FRANZ SCHWABL
QUANTU
M MECHANICS
FOURTH EDITION
WITH 123 FIGURES, 16 TABLES,
NUMEROUS WORKED EXAMPLES AND 127 PROBLEMS
YJ.
SPRINGER
TABLE OF CONTENTS
1. HISTORICA
L
AN
D
EXPERIMENTA
L
FOUNDATION
S
1
1.1 INTRODUCTION AND OVERVIEW 1
1.2 HISTORICALLY FUNDAMENTAL EXPERIMENTS AND INSIGHTS 3
1.2.1 PARTICLE PROPERTIES OF ELECTROMAGNETIC WAVES 3
1.2.2 WAVE PROPERTIES OF PARTICLES,
DIFFRACTION OF MATTE
R WAVES 7
1.2.3 DISCRETE STATES 8
2. TH
E WAVE FUNCTIO
N AN
D TH
E SCHRODINGE
R EQUATIO
N
13
2.1 THE WAVE FUNCTION AND ITS PROBABILITY INTERPRETATION 13
2.2 THE SCHRODINGER EQUATION FOR FREE PARTICLES 15
2.3 SUPERPOSITION OF PLANE WAVES 16
2.4 THE PROBABILITY DISTRIBUTION FOR A MEASUREMENT
OF MOMENTUM 19
2.4.1 ILLUSTRATION OF TH
E UNCERTAINTY PRINCIPLE 21
2.4.2 MOMENTUM IN-COORDINATE SPACE 22
2.4.3 OPERATORS AND THE SCALAR PRODUC
T 23
2.5 THE CORRESPONDENCE PRINCIPLE AND TH
E SCHRODINGER EQUATION 26
2.5.1 THE CORRESPONDENCE PRINCIPLE 26
2.5.2 THE POSTULATES OF QUANTUM THEORY 27
2.5.3 MANY-PARTICLE SYSTEMS 28
2.6 THE EHRENFEST THEOREM 28
2.7 THE CONTINUITY EQUATION FOR TH
E PROBABILITY DENSITY 31
2.8 STATIONARY SOLUTIONS OF THE SCHRODINGER EQUATION,
EIGENVALUE EQUATIONS 32
2.8.1 STATIONARY STATES 32
2.8.2 EIGENVALUE EQUATIONS . 33
2.8.3 EXPANSION IN STATIONARY STATES 35
2.9 THE PHYSICAL SIGNIFICANCE OF TH
E EIGENVALUES OF AN OPERATOR 36
2.9.1 SOME CONCEPTS FROM PROBABILITY THEORY 36
2.9.2 APPLICATION T
O OPERATORS WITH DISCRETE EIGENVALUES 37
2.9.3 APPLICATION T
O OPERATORS
WITH A CONTINUOUS SPECTRUM 38
2.9.4 AXIOMS OF QUANTUM THEORY 40
X TABLE OF CONTENTS
2.10 ADDITIONAL POINTS 41
2.10.1 THE GENERAL WAVE PACKET 41
2.10.2 REMARK ON TH
E NORMALIZABILITY
OF TH
E CONTINUUM STATES 43
PROBLEMS 44
3
. ONE-DIMENSIONA
L PROBLEM
S
47
3.1 THE HARMONIC OSCILLATOR T 47
3.1.1 THE ALGEBRAIC METHOD 48
3.1.2 THE HERMITE POLYNOMIALS 52
3.1.3 TH
E ZERO-POINT ENERGY 54
3.1.4 COHERENT STATES 56
3.2 POTENTIAL STEPS 58
3.2.1 CONTINUITY OF
IP(X)
AND
TJJ'{X)
FOR A PIECEWISE CONTINUOUS POTENTIAL 58
3.2.2 TH
E POTENTIAL STEP 59
3.3 TH
E TUNNELING EFFECT, TH
E POTENTIA
L BARRIER 64
3.3.1 THE POTENTIAL BARRIER 64
3.3.2 TH
E CONTINUOUS POTENTIAL BARRIER 67
3.3.3 EXAMPLE OF APPLICATION: A-DECAY 68
3.4 THE POTENTIAL WELL 71
3.4.1 EVEN SYMMETRY 72
3.4.2 ODD SYMMETRY 73
3.5 SYMMETRY PROPERTIES 76
3.5.1 PARIT
Y 76
3.5.2 CONJUGATION 77
3.6 GENERAL DISCUSSION
OF TH
E ONE-DIMENSIONAL SCHRODINGER EQUATION 77
3.7 THE POTENTIAL WELL, RESONANCES 81
3.7.1 ANALYTIC PROPERTIES OF TH
E TRANSMISSION COEFFICIENT. 83
3.7.2 THE MOTION OF A WAVE PACKET NEAR A RESONANCE .
. 87
PROBLEMS , 92
4
. TH
E UNCERTAINT
Y RELATIO
N
97
4.1 TH
E HEISENBERG UNCERTAINTY RELATION 97
4.1.1 THE SCHWARZ INEQUALITY 97
4.1.2 THE GENERAL UNCERTAINTY RELATION 97
4.2 ENERGY-TIME UNCERTAINTY 99
4.2.1 PASSAGE TIME AND ENERGY UNCERTAINTY 100
4.2.2 DURATION OF AN ENERGY MEASUREMENT
AND ENERGY UNCERTAINTY 100
4.2.3 LIFETIME AND ENERGY UNCERTAINTY 101
4.3 COMMON EIGENFUNCTIONS OF COMMUTING OPERATORS 102
PROBLEMS . . . .
' 106
TABLE OF CONTENTS ' XI
5. ANGULAR MOMENTU
M
107
5.1 COMMUTATION RELATIONS, ROTATIONS 107
5.2 EIGENVALUES OF ANGULAR MOMENTUM OPERATORS . .-. 110
5.3 ORBITAL ANGULAR MOMENTUM IN POLAR COORDINATES 112
PROBLEMS 118
6. THE CENTRAL POTENTIA
L I
119
6.1 SPHERICAL COORDINATES 119
6.2 BOUND STATES IN THREE DIMENSIONS 122
6.3 THE COULOMB POTENTIAL 124
6.4 THE TWO-BODY PROBLEM 138
PROBLEMS 140
7. MOTIO
N IN A
N ELECTROMAGNETI
C FIEL
D
.
V
143
7.1 THE HAMILTONIAN 143
7.2 CONSTANT MAGNETIC FIELD
B
144
7.3 THE NORMAL ZEEMAN EFFECT 145
7.4 CANONICAL AND KINETIC MOMENTUM, GAUGE TRANSFORMATION. 147
7.4.1 CANONICAL AND KINETIC MOMENTUM 147
7.4.2 CHANGE OF THE WAVE FUNCTION
UNDER A GAUGE TRANSFORMATION 148
7.5 THE AHARONOV-BOHM EFFECT 149
7.5.1 THE WAVE FUNCTION IN A REGION
FREE OF MAGNETIC FIELDS 149
7.5.2 THE AHARONOV-BOHM INTERFERENCE EXPERIMENT 150
7.6 FLUX QUANTIZATION IN SUPERCONDUCTORS 153
7.7 FREE ELECTRONS IN A MAGNETIC FIELD 154
PROBLEMS 155
8. OPERATORS, MATRICES
, STAT
E VECTOR
S
159
8.1 MATRICES, VECTORS, AND UNITARY TRANSFORMATIONS 159
8.2 STATE VECTORS AND DIRAC NOTATION 164
8.3 THE AXIOMS OF QUANTUM MECHANICS 169
8.3.1 COORDINATE REPRESENTATION 170
8.3.2 MOMENTUM REPRESENTATION 171
8.3.3 REPRESENTATION IN TERMS OF A DISCRETE BASIS SYSTEM 172
8.4 MULTIDIMENSIONAL SYSTEMS S,
AND MANY-PARTICLE SYSTEMS 172
8.5 THE SCHRODINGER, HEISENBERG
AND INTERACTION REPRESENTATIONS 173
8.5.1 THE SCHRODINGER REPRESENTATION 173
8.5.2 THE HEISENBERG REPRESENTATION 174
8.5.3 THE INTERACTION PICTURE (OR DIRAC REPRESENTATION) . 176
8.6 THE MOTION OF A FREE ELECTRON IN A MAGNETIC FIELD 177
PROBLEMS 181
XII TABLE OF CONTENTS
9. SPIN
183
9.1 THE EXPERIMENTAL DISCOVERY
OF THE INTERNAL ANGULAR MOMENTUM 183
9.1.1 THE "NORMAL" ZEEMAN EFFECT 183
9.1.2 THE STERN-GERLACH EXPERIMENT 183
9.2 MATHEMATICAL FORMULATION FOR SPIN-1/2 185
9.3 PROPERTIES OF THE PAULI MATRICES ^ 186
9.4 STATES, SPINORS " 187
9.5 MAGNETIC MOMENT 188
9.6 SPATIAL DEGREES OF FREEDOM AND SPIN 189
PROBLEMS 191
10. ADDITIO
N OF ANGULAR MOMENT
A
193
10.1 POSING THE PROBLEM 193
10.2 ADDITION OF SPIN-1/2 OPERATORS 194
10.3 ORBITAL ANGULAR MOMENTUM AND SPIN 1/2 196
10.4 THE GENERAL CASE 198
PROBLEMS 201
11
. APPROXIMATIO
N METHOD
S FOR STATIONAR
Y STATE
S
203
11.1 TIME INDEPENDENT PERTURBATION THEORY
(RAYLEIGH-SCHRODINGER) 203
11.1.1 NONDEGENERATE PERTURBATION THEORY 204
11.1.2 PERTURBATION THEORY FOR DEGENERATE STATES 206
11.2 THE VARIATIONAL PRINCIPLE 207
11.3 THE WKB (WENTZEL-KRAMERS-BRILLOUIN) METHOD 208
11.4 BRILLOUIN-WIGNER PERTURBATION THEORY 211
PROBLEMS
(
212
12
.
RELATIVISTI
C CORRECTION
S
215
12.1 RELATIVISTIC KINETIC ENERGY '. .
. 215
12.2 SPIN-ORBIT COUPLING 217
12.3 THE DARWIN TERM 219
12.4 FURTHER CORRECTIONS 222
12.4.1 THE LAMB SHIFT 222
12.4.2 HYPERFINE STRUCTURE 222
PROBLEMS
*" 225
13
.
SEVERAL-ELECTRO
N ATOM
S
227
13.1 IDENTICAL PARTICLES 227
13.1.1 BOSONS AND FERMIONS 227
13.1.2 NONINTERACTING PARTICLES 230
13.2 HELIUM .
/
. 233
13.2.1 WITHOUT THE ELECTRON-ELECTRON INTERACTION 233
TABLE OF CONTENTS XIII
13.2.2 ENERGY SHIFT
DUE T
O THE REPULSIVE ELECTRON-ELECTRON INTERACTION 235
13.2.3 THE VARIATIONAL METHOD : 240
13.3 THE HARTREE AND HARTREE-FOCK APPROXIMATIONS
(SELF-CONSISTENT FIELDS) 241
13.3.1 THE HARTREE APPROXIMATION 242
13.3.2 THE HARTREE-FOCK APPROXIMATION 244
13.4 THE THOMAS-FERMI METHOD . . .
' 247
13.5 ATOMIC STRUCTURE AND HUND'S RULES 252
PROBLEMS 258
14. TH
E ZEEMA
N EFFECT AN
D TH
E STARK EFFECT
259
14.1 THE HYDROGEN ATOM IN A MAGNETIC FIELD 259
14.1.1 WEAK FIELD 260
14.1.2 STRONG FIELD, THE PASCHEN-BACK EFFECT 260
14.1.3 THE ZEEMAN EFFECT FOR AN ARBITRARY MAGNETIC FIELD 261
14.2 MULTIELECTRON ATOMS 264
14.2.1 WEAK MAGNETIC FIELD 264
14.2.2 STRONG MAGNETIC FIELD, THE PASCHEN-BACK EFFECT . . . 266
14.3 THE STARK EFFECT 266
14.3.1 ENERGY SHIFT OF THE GROUND STAT
E 267
14.3.2 EXCITED STATES 267
PROBLEMS ' 269
15. MOLECULE
S
271
15.1 QUALITATIVE CONSIDERATIONS 271
15.2 THE BORN-OPPENHEIMER APPROXIMATION 273
15.3 THE HYDROGEN MOLECULAR ION (H^) 275
15.4 THE HYDROGEN MOLECULE H
2
' 278
15.5 ENERGY LEVELS OF A TWO-ATOM MOLECULE:
VIBRATIONAL AND ROTATIONAL LEVELS 282
15.6 THE VAN DER WAALS FORCE 284
PROBLEMS 287
16. TIM
E DEPENDEN
T PHENOMEN
A
289
16.1 THE HEISENBERG PICTUR
E FOR A TIME DEPENDENT HAMILTONIAN. 289
16.2 THE SUDDEN APPROXIMATION T 291
16.3 TIME DEPENDENT PERTURBATIO
N THEORY 292
16.3.1 PERTURBATIVE EXPANSION , 292
16.3.2 FIRST-ORDER TRANSITIONS 294
16.3.3 TRANSITIONS INTO A CONTINUOUS SPECTRUM,
THE GOLDEN RULE 294
16.3.4 PERIODIC PERTURBATION
S 297
16.4 INTERACTION WITH THE RADIATION FIELD 298
16.4.1 THE HAMILTONIAN 298
XIV TABLE OF CONTENTS
16.4.2 QUANTIZATION OF THE RADIATION FIELD 299
16.4.3 SPONTANEOUS EMISSION 301
16.4.4 ELECTRIC DIPOLE
(EL)
TRANSITIONS 303
16.4.5 SELECTION RULES FOR ELECTRIC DIPOLE
(EL)
TRANSITIONS 303
16.4.6 THE LIFETIME FOR ELECTRIC DIPOLE TRANSITIONS 306
16.4.7 ELECTRIC QUADRUPOLE
AND MAGNETIC DIPOLE TRANSITIONS 307
16.4.8 ABSORPTION AND INDUCED EMISSION 309
PROBLEMS : 310
17. TH
E CENTRAL POTENTIA
L II
313
17.1 THE SCHRODINGER EQUATION
FOR A SPHERICALLY SYMMETRIC SQUARE WELL 313
17.2 SPHERICAL BESSEL FUNCTIONS 314
17.3 BOUND STATES OF TH
E SPHERICAL POTENTIAL WELL 316
17.4 THE LIMITING CASE OF A DEEP POTENTIAL WELL 318
17.5 CONTINUUM SOLUTIONS FOR THE POTENTIAL WELL 320
17.6 EXPANSION OF PLANE WAVES IN SPHERICAL HARMONICS 321
PROBLEMS 324
18. SCATTERIN
G THEOR
Y
325
18.1 SCATTERING OF A WAVE PACKET AND STATIONARY STATES 325
18.1.1 THE WAVE PACKET 325
18.1.2 FORMAL SOLUTION
OF THE TIME INDEPENDENT SCHRODINGER EQUATION .
. 326
18.1.3 ASYMPTOTIC BEHAVIOR OF THE WAVE PACKET 328
18.2 THE SCATTERING CROSS SECTION 330
18.3 PARTIAL WAVES , 331
18.4 THE OPTICAL THEOREM'. 335
18.5 THE BORN APPROXIMATION 337
18.6 INELASTIC SCATTERING 339
18.7 SCATTERING PHASE SHIFTS 340
18.8 RESONANCE SCATTERING FROM A POTENTIAL WELL 342
18.9 LOW ENERGY S-WAVE SCATTERING; THE SCATTERING LENGTH 346
18.10 SCATTERING A
T HIGH ENERGIES 349
18.11 ADDITIONAL REMARKS 351
18.11.1 TRANSFORMATION TO THE LABORATORY FRAME 351
18.11.2 THE COULOMB POTENTIAL 352
PROBLEMS 352
19. SUPERSYMMETRI
C QUANTU
M THEOR
Y
355
19.1 GENERALIZED LADDER OPERATORS 355
19.2 EXAMPLES. 358
19.2.1 REFLECTION-FREE POTENTIALS 358
19.2.2 THE (5-FUNCTION 361
TABLE OF CONTENTS XV
19.2.3 THE HARMONIC OSCILLATOR 361
19.2.4 THE COULOMB POTENTIAL 362
19.3 ADDITIONAL REMARKS 365
PROBLEMS 367
20. STAT
E AND MEASUREMEN
T I
N QUANTU
M MECHANIC
S
369
20.
1
THE QUANTUM MECHANICAL STATE, CAUSALITY,
AND DETERMINISM .- 369
20.2 THE DENSITY MATRIX 371
20.2.1 THE DENSITY MATRIX FOR PURE AND MIXED ENSEMBLES 371
20.2.2 THE VON NEUMANN EQUATION 376
20.2.3 SPIN-1/2 SYSTEMS 377
20.3 THE MEASUREMENT PROCESS 380
20.3.1 THE STERN-GERLACH EXPERIMENT 380
20.3.2 THE QUASICLASSICAL SOLUTION 381
20.3.3 THE STERN-GERLACH EXPERIMENT
AS AN IDEALIZED MEASUREMENT : 381
20.3.4 A GENERAL EXPERIMENT
AND COUPLING T
O TH
E ENVIRONMENT 383
20.3.5 INFLUENCE OF AN OBSERVATION ON THE TIME EVOLUTION . 387
20.3.6 PHASE RELATIONS IN TH
E STERN-GERLACH EXPERIMENT. . 389
20.4 THE EPR ARGUMENT, HIDDEN VARIABLES, THE BELL INEQUALITY . 390
20.4.1 THE EP
R (EINSTEIN-PODOLSKY-ROSEN) ARGUMENT .
. 390
20.4.2 THE BELL INEQUALITY 392
PROBLEMS 396
APPENDI
X
399
A. MATHEMATICAL TOOLS FOR THE SOLUTION
OF LINEAR DIFFERENTIAL EQUATIONS 399
A.I THE FOURIER TRANSFORM 399
A.2 THE DELTA FUNCTION AND DISTRIBUTIONS 399
A.3 GREEN'S FUNCTIONS 404
B. CANONICAL AND KINETIC MOMENTUM 405
C. ALGEBRAIC DETERMINATION
OF THE ORBITAL ANGULAR MOMENTUM EIGENFUNCTIONS 406
D. THE PERIODIC TABLE AND IMPORTANT PHYSICAL QUANTITIES 412
SUBJECT INDEX
417 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Schwabl, Franz 1938-2009 |
| author_GND | (DE-588)120117312 |
| author_facet | Schwabl, Franz 1938-2009 |
| author_role | aut |
| author_sort | Schwabl, Franz 1938-2009 |
| author_variant | f s fs |
| building | Verbundindex |
| bvnumber | BV023177133 |
| classification_rvk | UK 1000 |
| ctrlnum | (OCoLC)315466882 (DE-599)DNB984910689 |
| 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 | 4. ed. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV023177133 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:00:13Z |
| indexdate | 2024-07-09T21:12:22Z |
| institution | BVB |
| isbn | 9783540719328 3540719326 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016363717 |
| oclc_num | 315466882 |
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| physical | XV, 424 S. Ill., graph. Darst. 24 cm |
| publishDate | 2007 |
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| publisher | Springer |
| record_format | marc |
| spelling | Schwabl, Franz 1938-2009 Verfasser (DE-588)120117312 aut Quantenmechanik Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems Franz Schwabl 4. ed. Berlin [u.a.] Springer 2007 XV, 424 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Bohmsche Quantenmechanik (DE-588)4414469-6 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Quantenmechanik (DE-588)4047989-4 s DE-604 Quantentheorie (DE-588)4047992-4 s 1\p DE-604 Bohmsche Quantenmechanik (DE-588)4414469-6 s 2\p DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016363717&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schwabl, Franz 1938-2009 Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems Bohmsche Quantenmechanik (DE-588)4414469-6 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4414469-6 (DE-588)4047992-4 (DE-588)4047989-4 (DE-588)4123623-3 |
| title | Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems |
| title_alt | Quantenmechanik |
| title_auth | Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems |
| title_exact_search | Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems |
| title_exact_search_txtP | Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems |
| title_full | Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems Franz Schwabl |
| title_fullStr | Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems Franz Schwabl |
| title_full_unstemmed | Quantum mechanics with ... 16 tables, numerous worked examples and 127 problems Franz Schwabl |
| title_short | Quantum mechanics |
| title_sort | quantum mechanics with 16 tables numerous worked examples and 127 problems |
| title_sub | with ... 16 tables, numerous worked examples and 127 problems |
| topic | Bohmsche Quantenmechanik (DE-588)4414469-6 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Bohmsche Quantenmechanik Quantentheorie Quantenmechanik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016363717&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schwablfranz quantenmechanik AT schwablfranz quantummechanicswith16tablesnumerousworkedexamplesand127problems |