Quantum mechanics: a modern and concise introductory course
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2012
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Graduate texts in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXII, 297 S. Ill., graph. Darst. |
| ISBN: | 9783642205552 9783642429507 9783642205569 |
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IMAGE 1
CONTENTS
1 INTRODUCTION 1
2 THE PRINCIPLES O F QUANTUM MECHANICS 5
2.1 CLASSICAL PHYSICS 5
2.2 MATHEMATICAL FRAMEWORK O F QUANTUM MECHANICS 6
2.3 BASIC PRINCIPLES O F QUANTUM MECHANICS 9
2.4 MEASUREMENT PROCESS 12
2.4.1 THE CONCEPT O F MEASUREMENT 12
2.4.2 QUANTUM MEASUREMENTS 13
2.5 SOME EXPERIMENTAL CONSEQUENCES OF THE BASIC PRINCIPLES 15
2.5.1 THOUGHT EXPERIMENTS 15
2.5.2 REAL TWO-SLIT EXPERIMENTS 19
2.6 OTHER CONSEQUENCES O F THE BASIC PRINCIPLES 21
2.6.1 COMMUTATION RELATIONS AND THE UNCERTAINTY PRINCIPLE 21
2.6.2 NO-CLONING THEOREM 23
2.6.3 COMMUTATION RELATIONS AND POISSON BRACKETS 24
2.7* PROPERTIES O F HILBERT SPACES AND OPERATORS 25
2.7.1 * SOME PROPERTIES O F HERMITIAN OPERATORS 27
2.7.2* UNITARY TRANSFORMATIONS 28
2.8* NOTIONS ON PROBABILITY THEORY 29
PROBLEMS 30
3 THE HEISENBERG REALIZATION O F QUANTUM MECHANICS 33
3.1 MATRIX FORMALISM 33
3.1.1 A REALIZATION O F THE HILBERT SPACE 33
3.1.2 SOLUTION O F THE EIGENVALUE EQUATION 35
3.2 TWO-DIMENSIONAL SPACES 36
X V L L
HTTP://D-NB.INFO/1010702750
IMAGE 2
XVIII CONTENTS
3.3 HARMONIC OSCILLATOR 39
3.3.1 SOLUTION O F THE EIGENVALUE EQUATION 39
3.3.2 SOME PROPERTIES O F THE SOLUTION 4 2
3.4 THE JAYNES-CUMMINGS MODEL 44
PROBLEMS 4 5
4 THE SCHRODINGER REALIZATION OF QUANTUM MECHANICS 47
4.1 TIME-INDEPENDENT SCHRODINGER EQUATION 47
4.1.1 PROBABILISTIC INTERPRETATION O F WAVE FUNCTIONS 4 9
4.2 THE HARMONIC OSCILLATOR REVISITED 51
4.2.1 SOLUTION O F THE SCHRODINGER EQUATION 52
4.2.2 SPATIAL FEATURES O F THE SOLUTIONS 5 3
4.3 FREE PARTICLE 55
4.4 ONE-DIMENSIONAL BOUND PROBLEMS 57
4.4.1 INFINITE SQUARE WELL POTENTIAL. ELECTRON GAS 57
4.4.2 FINITE SQUARE WELL POTENTIAL 5 9
4.5 ONE-DIMENSIONAL UNBOUND PROBLEMS 61
4.5.1 ONE-STEP POTENTIAL 61
4.5.2 SQUARE BARRIER 64
4.5.3 SCANNING TUNNELING MICROSCOPE 66
4.6^ BAND STRUCTURE OF CRYSTALS 68
PROBLEMS 70
5 MOTION IN ANGULAR SUBSPACE 73
5.1 EIGENVALUES AND EIGENSTATES 7 4
5.1.1 MATRIX TREATMENT 7 4
5.1.2 TREATMENT USING POSITION WAVE FUNCTIONS 75
5.2 SPIN 77
5.2.1 STERN-GERLACH EXPERIMENT 77
5.2.2 SPIN FORMALISM 79
5.3 OTHER FEATURES O F THE MOTION IN ANGULAR SUBSPACE 81
5.3.1 ADDITION O F ANGULAR MOMENTA 81
5.3.2^ ROTATIONS 83
5.3.3^ THE WIGNER-ECKART THEOREM 84
5.4* DETAILS OF THE MATRIX TREATMENT 85
5.5* DETAILS OF THE TREATMENT O F ORBITAL ANGULAR MOMENTUM 87
5.6* COUPLING WITH SPIN S = 1 / 2 89
PROBLEMS I 89
6 THREE-DIMENSIONAL HAMILTONIAN PROBLEMS 93
6.1 CENTRAL POTENTIALS 9 3
6.1.1 COULOMB AND HARMONIC OSCILLATOR POTENTIALS 9 4
6.1.2 RYDBERG ATOMS 9 6
6.2 SPIN-ORBIT INTERACTION 97
IMAGE 3
CONTENTS XIX
6.3 SOME ELEMENTS O F SCATTERING THEORY 99
6.3.1 BOUNDARY CONDITIONS 99
6.3.2 EXPANSION IN PARTIAL WAVES 100
6.3.3 CROSS SECTIONS 101
6.4* SOLUTIONS TO THE COULOMB AND OSCILLATOR POTENTIALS 102
6.5* SOME PROPERTIES O F SPHERICAL BESSEL FUNCTIONS 105
PROBLEMS 106
7 MANY-BODY PROBLEMS 109
7.1 THE PAULI PRINCIPLE 110
7.2 TWO-ELECTRON PROBLEMS 113
7.3 PERIODIC TABLES 114
7.3.1 THE ATOMIC CASE 114
7.3.2 THE NUCLEAR CASE 116
7.4 MOTION OF ELECTRONS IN SOLIDS 118
7.4.1 ELECTRON GAS 118
7.4.2 F BAND STRUCTURE O F CRYSTALS 120
7.4.3 F TRANSISTORS 121
7.4.4 F PHONONS IN LATTICE STRUCTURES 122
7.4.5* QUANTUM DOTS 125
7.5* BOSE-EINSTEIN CONDENSATION 127
7.6* QUANTUM HALL EFFECTS 129
7.6.1* INTEGER QUANTUM HALL EFFECT 130
7.6.2* FRACTIONAL QUANTUM HALL EFFECT 133
7.7* QUANTUM STATISTICS 134
7.8 F OCCUPATION NUMBER REPRESENTATION (SECOND QUANTIZATION) 136
PROBLEMS 139
8 APPROXIMATE SOLUTIONS TO QUANTUM PROBLEMS 141
8.1 PERTURBATION THEORY 141
8.2 VARIATIONAL PROCEDURE 144
8.3 GROUND STATE OF THE HE ATOM 144
8.4 MOLECULES 145
8.4.1 INTRINSIC MOTION: COVALENT BINDING 145
8.4.2 VIBRATIONAL AND ROTATIONAL MOTIONS 147
8.4.3 CHARACTERISTIC ENERGIES 149
8.5 APPROXIMATE MATRIX DIAGONALIZATIONS 150
8.5.1* APPROXIMATE TREATMENT OF PERIODIC POTENTIALS 151
8.6 INDEPENDENT-PARTICLE APPROXIMATIONS 152
8.6.1* THE HARTREE-FOCK APPROXIMATION 152
8.6.2* THE RANDOM-PHASE APPROXIMATION (RPA) 154
8.7* MATRIX ELEMENTS INVOLVING THE INVERSE OF THE INTERPARTICLE DISTANCE
156
PROBLEMS 157
IMAGE 4
XX CONTENTS
9 TIME DEPENDENCE IN QUANTUM MECHANICS 161
9.1 THE TIME PRINCIPLE 161
9.2 TIME DEPENDENCE OF SPIN STATES 164
9.2.1 LARMOR PRECESSION 164
9.2.2 MAGNETIC RESONANCE 165
9.3 SUDDEN CHANGE IN THE HAMILTONIAN 167
9.4 TIME-DEPENDENT PERTURBATION THEORY 168
9.5 ENERGY-TIME UNCERTAINTY RELATION 169
9.6* THE HEISENBERG PICTURE 171
9.7* TIME-REVERSAL SYMMETRY 172
9.8* QUANTUM ELECTRODYNAMICS FOR NEWCOMERS 172
9.8.1 * CLASSICAL DESCRIPTION O F THE RADIATION FIELD 173
9.8.2* QUANTIZATION OF THE RADIATION FIELD 174
9.8.3* INTERACTION O F LIGHT WITH PARTICLES 176
9.8.4* EMISSION AND ABSORPTION O F RADIATION 177
9.8.5* SELECTION RULES. 178
9.8.6* LASERS AND MASERS 179
PROBLEMS 181
10 BROKEN SYMMETRIES 183
10.1 THE BCS THEORY OF SUPERCONDUCTIVITY 184
10.1.1* THE CONJUGATE VARIABLE TO THE NUMBER O F PARTICLES 184 10.1.2*
THE MONOPOLE PAIRING OPERATOR AND THE HAMILTONIAN 186
10.1.3* THE BCS HAMILTONIAN 187
10.1.4* THE GROUND STATE 190
10.1.5* THE EXCITATION SPECTRUM 190
10.1.6* COLLECTIVE SECTOR. ROTATIONAL BANDS. JOSEPHSON JUNCTIONS 194
10.2 QUANTIZATION WITH CONSTRAINTS 195
10.2.1 CONSTRAINTS 195
10.2.2 OUTLINE O F THE BRST SOLUTION 197
10.2.3* A PRESENTATION OF THE BRST SYMMETRY FOR THE ABELIAN CASE 199
10.2.4* APPLICATION O F THE BRST FORMALISM TO THE ABELIAN TOY MODEL 200
10.3 GENERALIZATIONS 203
PROBLEMS 204
11 EIGENVECTORS O F THE POSITION OPERATOR PATH INTEGRAL FORMULATION .
207 11.1 T EIGENVECTORS O F THE POSITION OPERATOR AND THE DELTA FUNCTION
207
11.2* THE PROPAGATOR 209
11.2.1* THE FREE PARTICLE PROPAGATOR 210
11.3* PATH INTEGRAL FORMULATION O F QUANTUM MECHANICS 211
IMAGE 5
CONTENTS XXI
11.3.1* THE HARMONIC OSCILLATOR RE-REVISITED.
THE PATH INTEGRAL CALCULATION 214
11.3.2* THE CLASSICAL ACTION AND THE QUANTUM CORRECTION TO THE HARMONIC
OSCILLATOR 215
12 ENTANGLEMENT AND EXPERIMENTAL TESTS O F QUANTUM MECHANICS 219 12.1
ENTANGLEMENT 220
12.2 THE BELL STATES 221
12.3 EXPERIMENTAL TESTS O F QUANTUM MECHANICS 222
12.3.1 TWO-SLIT EXPERIMENTS REVISITED 223
12.3.2 EPR AND BELL INEQUALITIES 225
12.3.3 SINGLE QUANTUM SYSTEMS 227
12.3.4 A QUANTUM, MAN-MADE MECHANICAL OBJECT 230
13 QUANTUM INFORMATION 233
13.1 CONCEPTUAL FRAMEWORK 233
13.2 QUANTUM CRYPTOGRAPHY 234
13.3 TELEPORTATION 235
13.4* QUANTUM COMPUTATION 237
13.4.1* FACTORIZATION 237
13.5* QUANTUM GATES 239
13.5.1* ONE-QUBIT SYSTEMS 240
13.5.2* TWO-QUBIT SYSTEMS 241
13.5.3* N-QUBIT SYSTEMS 242
PROBLEMS 243
14 INTERPRETATIONS O F MEASUREMENTS. DECOHERENCE. DENSITY MATRIX 245
14.1 ORTHODOX INTERPRETATIONS 245
14.1.1 THE STANDARD INTERPRETATION 246
14.1.2 THE COPENHAGEN INTERPRETATION 247
14.2* THE EMERGENCE O F CLASSICALITY FROM THE QUANTUM SUBSTRATE.
DECOHERENCE 247
14.2.1 * A MATHEMATICAL MODEL O F DECOHERENCE 249
14.2.2* AN EXPERIMENT WITH DECOHERENCE 251
14.3* QUANTUM MEASUREMENTS 252
14.4 THE DENSITY MATRIX 254
14.4.1 MIXED DENSITY MATRIX 255
14.4.2 REDUCED DENSITY MATRIX 256
PROBLEMS 258
15 A BRIEF HISTORY O F QUANTUM MECHANICS 259
15.1 SOCIAL CONTEXT IN CENTRAL EUROPE DURING THE 1920S 259
15.2 PRE-HISTORY OF QUANTUM PHYSICS (1860 T 1900) 260
15.3 OLD QUANTUM THEORY (1900 T 1925) 261
15.3.1 RADIATION 261
15.3.2 MATTER 263
15.4 QUANTUM MECHANICS (1925 5 T 1928) 265
IMAGE 6
XXII CONTENTS
15.5 PHILOSOPHICAL ASPECTS 267
15.5.1 COMPLEMENTARITY PRINCIPLE 267
15.5.2 DISCUSSIONS BETWEEN BOHR AND EINSTEIN 268
15.6 RECENT QUANTUM MECHANICS 271
A SOLUTIONS TO PROBLEMS AND PHYSICAL CONSTANTS 275
REFERENCES 287
INDEX 291 |
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| isbn | 9783642205552 9783642429507 9783642205569 |
| language | English |
| lccn | 2012938371 |
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| spelling | Bès, Daniel R. 1931- Verfasser (DE-588)102583836X aut Quantum mechanics a modern and concise introductory course Daniel Bes 3. ed. Berlin [u.a.] Springer 2012 XXII, 297 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Hier auch später erschienene, unveränderte Nachdrucke Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3705622&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025401377&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bès, Daniel R. 1931- Quantum mechanics a modern and concise introductory course Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 |
| title | Quantum mechanics a modern and concise introductory course |
| title_auth | Quantum mechanics a modern and concise introductory course |
| title_exact_search | Quantum mechanics a modern and concise introductory course |
| title_full | Quantum mechanics a modern and concise introductory course Daniel Bes |
| title_fullStr | Quantum mechanics a modern and concise introductory course Daniel Bes |
| title_full_unstemmed | Quantum mechanics a modern and concise introductory course Daniel Bes |
| title_short | Quantum mechanics |
| title_sort | quantum mechanics a modern and concise introductory course |
| title_sub | a modern and concise introductory course |
| topic | Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Quantenmechanik |
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