Lectures on quantum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 307 S. Ill. 24 cm |
| ISBN: | 0387377425 9780387377421 0387377441 9780387377445 |
Internformat
MARC
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| 020 | |a 9780387377421 |9 978-0-387-37742-1 | ||
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| 044 | |a xxu |c US | ||
| 049 | |a DE-384 |a DE-1051 |a DE-703 | ||
| 050 | 0 | |a QC174.125 | |
| 082 | 0 | |a 530.12 | |
| 084 | |a UK 1000 |0 (DE-625)145785: |2 rvk | ||
| 100 | 1 | |a Basdevant, Jean-Louis |d 1939- |e Verfasser |0 (DE-588)133559130 |4 aut | |
| 245 | 1 | 0 | |a Lectures on quantum mechanics |c Jean-Louis Basdevant |
| 264 | 1 | |a New York |b Springer |c 2007 | |
| 300 | |a XVI, 307 S. |b Ill. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 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 | |
| 689 | 0 | 0 | |a Quantenmechanik |0 (DE-588)4047989-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016077239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016077239 | ||
Datensatz im Suchindex
| _version_ | 1804137131626463232 |
|---|---|
| adam_text | Contents
Preface
........................................................ xv
1
Praise of physics
........................................... 1
1.1
The interplay of the eye and the mind
...................... 1
1.2
Advanced technologies
................................... 5
1.3
The pillars of contemporary physics
........................ 0
1.3.1
Mysteries of light
.................................. 6
1.3.2
Fundamental structure
oí
matter
.................... 8
1.4
The infinitely complex
................................... 9
1.5
The Universe
........................................... 12
2
A quantum phenomenon
................................... 13
2.1
Wave behavior of particles
................................ 16
2.1.1
Interferences
...................................... 16
2.1.2
Wave behavior of matter
........................... 17
2.1.3
Analysis of the phenomenon
........................ 18
2.2
Probabilistic nature of quantum phenomena
................ 20
2.2.1
Random behavior of pa.iTides
....................... 20
2.2.2
A nondassical probabilistic phenomenon
............. 20
2.3
Conclusions
............................................. 21
2.-1
Phenomenologieal description
............................. 23
3
Wave function,
Schrödinger
equation
...................... 25
3.1
Terminology and methodology
............................ 25
3.1.1
Terminology
...................................... 25
3.1.2
Methodology
...................................... 26
3.2
Principles of wave mechanics
.............................. 27
3.2.1
The interference experiment
........................ 27
3.2.2
Wave function
.................................... 27
3.2.3 Schrödinger
equation
.............................. 2?)
3.3
Superposition principle
................................... 30
viii
Contents
3.4
Wave packets
. . ......................................... 31
3.4.1
Free wave packets
................................. 31
3.4.2
Fourier transformation
............................. 32
3.4.3
Shape of wave packets
............................. 33
3.5
Historical landmarks
..................................... 33
3.6
Momentum
probabilit}
law
............................... 35
3.6.1
Free particle
...................................... 35
3.6.2
General ease
.....................................: 36
3.7 Heisenberg
uncertainty relations
........................... 36
3.7.1
Size and energy of a quantum system
................ 37
3.7.2
Stability of matter
................................. 38
3.8
Controversies and paradoxes
.............................. 40
3.8.1
The
1927
Solvay Congress
.......................... 40
3.8.2
The EPR paradox
................................. 41
3.8.3
Hidden variables. Bell s inequalities
.................. 41
3.8.4
The experimental test
.............................. 42
4
Physical quantities
......................................... 45
1.1
Statement of the problem
................................. 46
4.1.1
Physical quantities
................................ 46
4.1.2
Position and momentum
........................... 47
4.2
Observables
............................................. 48
4.2.1
Position observable
................................ 49
4.2.2
Momentum observable
............................. 49
4.2.3
Correspondence principle
........................... 50
4.2.4
Historical landmarks
............................... 50
4.3
A counterexample of Einstein and its consequences
.......... 51
4.3.1
What do we know after a measurement?
............. 53
4.3.2
Eigenstates and eigenvalues of an observable;
.......... 54
4.3.3
Wave packet reduction
............................. 55
4.4
The specific role of energy
................................ 56
4.4.1
The Hamil
toi
lian..................................
56
4.4.2
The
Schrödinger
equation, time and energy
........... 57
4.4.3
Stationary states
.................................. 58
4.4.4
Motion:
Interference
of stationary states
.............. 59
4.5 Schrödinger
s
cat
........................................ 60
4.5.1
The dreadful idea
.................................. 60
4.5.2
The classical world
................................ 63
5
Energy quantization
....................................... 65
5.1
Methodology
............................................ 65
5.1.1
Bound states and scattering states
................... 66
5.1.2
One-dimensional problems
.......................... 67
5.2
The harmonic oscillator
.................................. 67
5.2.1
Harmonic potential
................................ 67
Contents
ix
5.2.2
Energy
levels, eigenfunetions
........................ 68
5.3
Square
well potentials....................................
69
5.3.1
Square potentials
.................................■. 69
5.3.2
Symmetric square well
............................. 70
5.3.3
Infinite well, particle in a box
....................... 73
5.4
Double well, the ammonia molecule
........................ 74
5.4.1
The model
........................................ 74
5.4.2
Stationary states, the tunnel effect
................... 75
5.4.3
Energy levels
..................................... 76
5.4.4
Wave functions
.................................... 78
5.4.5
Inversion of the molecule
........................... 79
5.5
Illustrations and applications of the tunnel effect
............ 81
5.5.1
Sensitivity to the parameters
....................... 81
5.5.2
Molecular structure
................................ 82
5.6
Tunneling microscopy, nauotechnologies
.................... 84
5.6.1 Nanotechnologie*.................................. 84
r.
>.6.2 Classical limit
..................................... 85
6
Principles of quantum mechanics
.......................... 87
6.1
Hubert space
........................................... 88
G.I.I Two-dimensional space
............................. 89
6.1.2
Square
integrable
functions
......................... 89
6.2
Dirac formalism
......................................... 92
6.2.1
Notations
........................................ 92
6.2.2
Operators
........................................ 93
6.2.3
Syntax rules
...................................... 95
6.2.4
Projectors; decomposition of the identity
............. 95
6.3
Measurement results
..................................... 96
6.3.1
Eigenvectors and eigenvalues of an observable
......... 96
6.3.2
Results of the measurement of a physical quantity
..... 97
6.3.3
Probabilities
...................................... 98
6.3.4
The Riesz spectral theorem
......................... 98
6.3.5
Physical meaning of various representations
...........100
6.4
Principles of quantum mechanics
..........................101
6.4.1
The principles
....................................101
6.4.2
The case of a continuous spectrum
...................102
6.4.3
Interest of this synthetic formulation
.................102
6.5 Heisenberg^
matrices
....................................103
6.5.1
Matrix representation of operators
...................103
6.5.2
Matrices X and
Ρ
.................................104
6.5.3
Heisenberg s thoughts
..............................104
6.6
The polarization of light, quantum logic
..................107
χ
Contents
7
Two-state systems
.........................................113
7.1
The NH3 molecule?
.......................................113
7.2
Two-state
system
......................................114
7.3
Matrix quantum mechanics
...............................116
7.3.1
Vedora
..........................................116
7.3.2
Hamiltom an
......................................117
7.3.3
Observables
......................................
J
! 7
7.3.4
Examples
........................................119
7.3.5
Basis of classical configurations
.....................119
7.3.6
Interference! and measurement
.......................120
7.4
NIÏ3
in an eleciric field
...................................120
7.4.1
Uniform constant field
.............................121
7.4.2
Weak and strong field regimes
......................122
7.4.3
Other two-state systems
............................123
7.5
The ammonia molecule in an in homogeneous field
...........123
7.5.1
Force? on
t
lie molecule? in an inhomogeneous field
......124
7.5.2
Population inversion
...............................126
7.6
Reaction to an oscillating field,
tłu? maser ..................
126
7.7
Principle and applications of the?
maser
.....................128
7.7.1
Amplifiers
........................................129
7.7.2
Oscillators
........................................130
7.7.3
Atomic clocks
.....................................130
7.7.4
Tests of relativity
.................................132
7.8
Neutrino oscillations
.....................................134
7.8.1
Lept
елі
familie?«
...................................134
7.8.2
Mechanism of the ejaculations: reactor neutrinos
.......135
7.8.3
Successive hermapliroditisin of neutrinos
.............138
8
Algebra of
observables
.....................................143
8. 1
Commutation
oí observables..............................
143
8.1.1
Fundamental commutation relation
..................143
8.1.2
Other
commutai
ion relations
.......................144
8.1.3
Dirac in the summer of
1925........................145
8.2
Uncertainty relations
.....................................146
8.3
Evolution of physical quantities
...........................147
8.3.1
Evolution of an expectation value
...................147
8.3.2
Particle in a pejtemtial. classical limit
.................148
8.3.3
Oonse?rvatie)ii laws
.................................149
8.4
Algebraic resolution of the harmonic oscillator
..............150
8.4.1
Operators
ά.
(Vі
.
anel
Ñ
............................151
8.4.2
Determination e>f the eigenvalues
....................151
8.4.3
Eigenstates
.......................................152
8.5
Commuting
observables
..................................154
8.5.1
Theorem
.........................................154
8.5.2
Example
.........................................155
Contents xi
6.
б.
3
Tensor structure of quantum mechanics
..............155
8.5.4
Complete set of commuting
observables (CSCO)
......156
8.5.5
Completely prepared quantum state
.................157
8.6
Sunday. September
20. 1925 ..............................158
9
Angular momentum
.......................................161
9.1
Fundamental commutation relation
........................162
9.1.1
Classical angular momentum
........................162
9.1.2
Definition of an angular momentum observable
........162
9.1.3
Results of the quantization
.........................163
9.2
Proof of the quantization
.................................16.3
9.2.1
Statement of the problem
..........................163
9.2.2
Vectors j.m
>
and eigenvalues
j
and
m
.............164
9.2.3
Operators J±
= ./,.
± Uu
...........................165
9.2.4
Quantization
......................................166
9.3
Orbital angular momenta
.................................168
9.3.1
Formulae in spherical coordinates
...................168
9.3.2
Integer values of
m
and
(:...........................168
9.3.3
Spherical harmonics
...............................169
9.4
Rotation energy of a diatomic molecule
.....................170
9.4.1
Diatomic molecule
.................................171
9.4.2
The CO molecule
..................................172
9.5
Angular momentum and magnetic moment
.................173
9.5.1
Classical model
...................................173
9.5.2
Quantum transposition
.............................175
9.5.3
Experimental consequences
.........................175
9.5.4
L
armor precession
.................................176
9.5.5
What about half-integer values of
j
and m?
...........177
10
The Hydrogen Atom
.......................................179
10.1
Two-body problem; relative1 motion
........................180
10.2
Motion in a central potential
..............................182
10.2.1
Spherical coordinates. CSCO .;
.....................182
10.2.2
Eigenfunctions common to H.
І,·2.
and Lz
............182
10.2.3
Quantum numbers
.................................183
10.3
The hydrogen atom
......................................186
10.3.1
Atomic units:
fint1
structure constant
.................186
10.3.2
Тік4
dimension less radial equation
...................188
10.3.3
Spectrum of hydrogen
..............................191
10.3.4
Stationary states of the hydrogen atom
...............191
10.3.5
Dimensions and orders of magnitude
.................193
10.3.6
Historical landmarks
...............................194
10.4
Muonic atoms
...........................................195
xii Contents
11
Spin
1/2...................................................199
11.1
Experimental results
.....................................199
11.2
Spin
1/2
formalism
......................................200
11.2.1
Representation in a particular basis
..................201
11.2.2
Matrix representation
.............................201
11.3
Complete description of a spin
1/2
particle
.................202
11.3.1
Observables
......................................203
11.4
Physical spin effects
.....................................204
11
.õ
Spin magnetic moment
...................................205
11.5.1
Hamiltonian of a one-electron atom
..................205
11.6
The Stern- Gerlach experiment
............................206
11.6.1
Principle of the experiment
.........................206
11.6.2
Semi-classical analysis
.............................207
11.6.3
Experimental results
...............................208
11.6.4
Explanation of the Stern-Gerlach experiment
.........208
11.6.5
Successive Stern Gerlach setups
.....................211
11.6.6
Measurement, along an arbitrary axis
.................211
1.1.7
The discovery of spin
....................................213
11.7.1
The hidden sides of the Stern-Gerlach experiment
.....213
11.7.2
Einstein and
Ehrenfest
s objections
..................215
11.7-.3 Anomalous
Zeeman
effect
..........................216
11.7.4
Bohr s challenge to
Pauli...........................217
11.7.5
The spin hypothesis
...............................217
11.7.6
The fine structure of atomic lines
....................218
11.8
Magnetism, magnetic resonance
...........................219
11.8.1
Spin effects, Larmor precession
......................220
11.8.2
Larmor precession in a fixed magnetic field
...........221
11.8.3
Rabrs calculation and experiment
...................221
11.8.4
Nuclear magnetic resonance
........................225
11.8.5
Magnetic moments of elementary particles
............227
11.9
Entertainment: Rotation by
2тг
of a spin
1/2................228
12
The
Pauli
Principle
........................................229
12.1
Indistinguishability of two identical particles
................230
12.1.1
Identical particles in classical physics
................230
12.1.2
The quantum problem
.............................230
12.1.3
Example of ambiguities
............................231
12.2
Systems of two spin
1/2
particles, total spin
................232
12.2.1
The Hubert space of the problem
....................232
12.2.2
Hubert space of spin variables
.......................232
1.2.2.3
Matrix representation
..............................233
12.2.4
Total spin states
..................................233
12.3
Two-particle system; the exchange operator
.................235
12.3.1
The Hubert space1 for the two-particle .system
.........235
12.3.2
The exchange operator between identical particles
.....236
Contents xiii
12.3.3
Symmetry of the states
............................237
12.4
The
Pauli
principle
......................................238
12.4.1
The case of two particles
...........................238
12.4.2
Independent
fermions
and exclusion principle
.........239
12.4.3
The case of
N
identical particles
....................239
12.5
Physical consequences of the
Pauli
principle
.................241
12.5.1
Exchange force between two
fermions
................241
12.5.2
The ground state of
N
identical independent particles.
. 241
12.5.3
Behavior of fermion and boson systems at
low7 temperatures
..................................243
13
Entangled states: The way of paradoxes
...................247
13.1
The EPR paradox
.......................................247
13.2
The version of David
Bohm
...............................249
13.2.1
Bell s inequality
...................................251
13.2.2
Experimental tests
................................254
13.3
Quantum cryptography: how to enjoy a nuisance
............256
13.3.1
The communication between Alice and Bob
...........256
13.3.2
Present experimental setups
........................258
13.4
Quantum
teleportat
ion
...................................260
13.4.1
Bell states
........................................260
13.4.2
Teleportation
.....................................261
14
Quantum mechanics in the Universe
.......................263
14.1
Quantum mechanics and astronomy
........................265
14.1.1
Life and death of stars
.............................265
14.1.2
Spectroscopy
.....................................268
14.2
Radioastronoiny, the interstellar medium
...................268
14.2.1
The interstellar medium
............................269
14.3
Cosmic background radiation: Birth of the Universe
..........273
14.4
The 21-cm line of hydrogen
...............................275
14.4.1
Hyperfine structure of hydrogen
.....................276
14.4.2
Hydrogen
maser
...................................278
14.4.3
Importance of the 21-cm Hue
........................279
14.5
The Milky Way
.........................................280
14.6
The intergalactic medium: star wars
.......................281
14.6.1
Spiral arms, birthplaces of stars
.....................285
14.7
Interstellar molecules, the origin of life
.....................287
14.7.1
Rotation spectra of molecules
.......................287
14.7.2
Interstellar molecules
..............................288
14.7.3
The origin of life
..................................289
14.8
Where are they? Quantum mechanics, the tmiversal
cosmic language
.........................................291
14.8.1
Life, intelligence, and thought
.......................291
14.8.2
Listening to extraterrestrials
........................293
xiv Contents
14.8.3
Quantum mechanics, the universal cosmic language
.... 295
Index
..........................................................3Ü3
|
| adam_txt |
Contents
Preface
. xv
1
Praise of physics
. 1
1.1
The interplay of the eye and the mind
. 1
1.2
Advanced technologies
. 5
1.3
The pillars of contemporary physics
. 0
1.3.1
Mysteries of light
. 6
1.3.2
Fundamental structure
oí'
matter
. 8
1.4
The infinitely complex
. 9
1.5
The Universe
. 12
2
A quantum phenomenon
. 13
2.1
Wave behavior of particles
. 16
2.1.1
Interferences
. 16
2.1.2
Wave behavior of matter
. 17
2.1.3
Analysis of the phenomenon
. 18
2.2
Probabilistic nature of quantum phenomena
. 20
2.2.1
Random behavior of pa.iTides
. 20
2.2.2
A nondassical probabilistic phenomenon
. 20
2.3
Conclusions
. 21
2.-1
Phenomenologieal description
. 23
3
Wave function,
Schrödinger
equation
. 25
3.1
Terminology and methodology
. 25
3.1.1
Terminology
. 25
3.1.2
Methodology
. 26
3.2
Principles of wave mechanics
. 27
3.2.1
The interference experiment
. 27
3.2.2
Wave function
. 27
3.2.3 Schrödinger
equation
. 2?)
3.3
Superposition principle
. 30
viii
Contents
3.4
Wave packets
. . . 31
3.4.1
Free wave packets
. 31
3.4.2
Fourier transformation
. 32
3.4.3
Shape of wave packets
. 33
3.5
Historical landmarks
. 33
3.6
Momentum
probabilit}"
law
. 35
3.6.1
Free particle
. 35
3.6.2
General ease
.: 36
3.7 Heisenberg
uncertainty relations
. 36
3.7.1
Size and energy of a quantum system
. 37
3.7.2
Stability of matter
. 38
3.8
Controversies and paradoxes
. 40
3.8.1
The
1927
Solvay Congress
. 40
3.8.2
The EPR paradox
. 41
3.8.3
Hidden variables. Bell's inequalities
. 41
3.8.4
The experimental test
. 42
4
Physical quantities
. 45
1.1
Statement of the problem
. 46
4.1.1
Physical quantities
. 46
4.1.2
Position and momentum
. 47
4.2
Observables
. 48
4.2.1
Position observable
. 49
4.2.2
Momentum observable
. 49
4.2.3
Correspondence principle
. 50
4.2.4
Historical landmarks
. 50
4.3
A counterexample of Einstein and its consequences
. 51
4.3.1
What do we know after a measurement?
. 53
4.3.2
Eigenstates and eigenvalues of an observable;
. 54
4.3.3
Wave packet reduction
. 55
4.4
The specific role of energy
. 56
4.4.1
The Hamil
toi
lian.
56
4.4.2
The
Schrödinger
equation, time and energy
. 57
4.4.3
Stationary states
. 58
4.4.4
Motion:
Interference
of stationary states
. 59
4.5 Schrödinger
s
cat
. 60
4.5.1
The dreadful idea
. 60
4.5.2
The classical world
. 63
5
Energy quantization
. 65
5.1
Methodology
. 65
5.1.1
Bound states and scattering states
. 66
5.1.2
One-dimensional problems
. 67
5.2
The harmonic oscillator
. 67
5.2.1
Harmonic potential
. 67
Contents
ix
5.2.2
Energy
levels, eigenfunetions
. 68
5.3
Square
well potentials.
69
5.3.1
Square potentials
.■. 69
5.3.2
Symmetric square well
. 70
5.3.3
Infinite well, particle in a box
. 73
5.4
Double well, the ammonia molecule
. 74
5.4.1
The model
. 74
5.4.2
Stationary states, the tunnel effect
. 75
5.4.3
Energy levels
. 76
5.4.4
Wave functions
. 78
5.4.5
Inversion of the molecule
. 79
5.5
Illustrations and applications of the tunnel effect
. 81
5.5.1
Sensitivity to the parameters
. 81
5.5.2
Molecular structure
. 82
5.6
Tunneling microscopy, nauotechnologies
. 84
5.6.1 Nanotechnologie*. 84
r.
>.6.2 Classical limit
. 85
6
Principles of quantum mechanics
. 87
6.1
Hubert space
. 88
G.I.I Two-dimensional space
. 89
6.1.2
Square
integrable
functions
. 89
6.2
Dirac formalism
. 92
6.2.1
Notations
. 92
6.2.2
Operators
. 93
6.2.3
Syntax rules
. 95
6.2.4
Projectors; decomposition of the identity
. 95
6.3
Measurement results
. 96
6.3.1
Eigenvectors and eigenvalues of an observable
. 96
6.3.2
Results of the measurement of a physical quantity
. 97
6.3.3
Probabilities
. 98
6.3.4
The Riesz spectral theorem
. 98
6.3.5
Physical meaning of various representations
.100
6.4
Principles of quantum mechanics
.101
6.4.1
The principles
.101
6.4.2
The case of a continuous spectrum
.102
6.4.3
Interest of this synthetic formulation
.102
6.5 Heisenberg^
matrices
.103
6.5.1
Matrix representation of operators
.103
6.5.2
Matrices X and
Ρ
.104
6.5.3
Heisenberg's thoughts
.104
6.6
The polarization of light, quantum "logic"
.107
χ
Contents
7
Two-state systems
.113
7.1
The NH3 molecule?
.113
7.2
"Two-state
"
system
.114
7.3
Matrix quantum mechanics
.116
7.3.1
Vedora
.116
7.3.2
Hamiltom'an
.117
7.3.3
Observables
.
J
! 7
7.3.4
Examples
.119
7.3.5
Basis of classical configurations
.119
7.3.6
Interference! and measurement
.120
7.4
NIÏ3
in an eleciric field
.120
7.4.1
Uniform constant field
.121
7.4.2
Weak and strong field regimes
.122
7.4.3
Other two-state systems
.123
7.5
The ammonia molecule in an in homogeneous field
.123
7.5.1
Force? on
t
lie molecule? in an inhomogeneous field
.124
7.5.2
Population inversion
.126
7.6
Reaction to an oscillating field,
tłu? maser .
126
7.7
Principle and applications of the?
maser
.128
7.7.1
Amplifiers
.129
7.7.2
Oscillators
.130
7.7.3
Atomic clocks
.130
7.7.4
Tests of relativity
.132
7.8
Neutrino oscillations
.134
7.8.1
Lept
елі
familie?«
.134
7.8.2
Mechanism of the ejaculations: reactor neutrinos
.135
7.8.3
Successive hermapliroditisin of' neutrinos
.138
8
Algebra of
observables
.143
8.'1
Commutation
oí observables.
143
8.1.1
Fundamental commutation relation
.143
8.1.2
Other
commutai
ion relations
.144
8.1.3
Dirac in the summer of
1925.145
8.2
Uncertainty relations
.146
8.3
Evolution of physical quantities
.147
8.3.1
Evolution of an expectation value
.147
8.3.2
Particle in a pejtemtial. classical limit
.148
8.3.3
Oonse?rvatie)ii laws
.149
8.4
Algebraic resolution of the harmonic oscillator
.150
8.4.1
Operators
ά.
(Vі
.
anel
Ñ
.151
8.4.2
Determination e>f the eigenvalues
.151
8.4.3
Eigenstates
.152
8.5
Commuting
observables
.154
8.5.1
Theorem
.154
8.5.2
Example
.155
Contents xi
6.
б.
3
Tensor structure of quantum mechanics
.155
8.5.4
Complete set of commuting
observables (CSCO)
.156
8.5.5
Completely prepared quantum state
.157
8.6
Sunday. September
20. 1925 .158
9
Angular momentum
.161
9.1
Fundamental commutation relation
.162
9.1.1
Classical angular momentum
.162
9.1.2
Definition of an angular momentum observable
.162
9.1.3
Results of the quantization
.163
9.2
Proof of the quantization
.16.3
9.2.1
Statement of the problem
.163
9.2.2
Vectors \j.m
>
and eigenvalues
j
and
m
.164
9.2.3
Operators J±
= ./,.
± Uu
.165
9.2.4
Quantization
.166
9.3
Orbital angular momenta
.168
9.3.1
Formulae in spherical coordinates
.168
9.3.2
Integer values of'
m
and
(:.168
9.3.3
Spherical harmonics
.169
9.4
Rotation energy of a diatomic molecule
.170
9.4.1
Diatomic molecule
.171
9.4.2
The CO molecule
.172
9.5
Angular momentum and magnetic moment
.173
9.5.1
Classical model
.173
9.5.2
Quantum transposition
.175
9.5.3
Experimental consequences
.175
9.5.4
L
armor precession
.176
9.5.5
What about half-integer values of
j
and m?
.177
10
The Hydrogen Atom
.179
10.1
Two-body problem; relative1 motion
.180
10.2
Motion in a central potential
.182
10.2.1
Spherical coordinates. CSCO .;
.182
10.2.2
Eigenfunctions common to H.
І,·2.
and Lz
.182
10.2.3
Quantum numbers
.183
10.3
The hydrogen atom
.186
10.3.1
Atomic units:
fint1
structure constant
.186
10.3.2
Тік4
dimension less radial equation
.188
10.3.3
Spectrum of hydrogen
.191
10.3.4
Stationary states of the hydrogen atom
.191
10.3.5
Dimensions and orders of magnitude
.193
10.3.6
Historical landmarks
.194
10.4
Muonic atoms
.195
xii Contents
11
Spin
1/2.199
11.1
Experimental results
.199
11.2
Spin
1/2
formalism
.200
11.2.1
Representation in a particular basis
.201
11.2.2
Matrix representation
.201
11.3
Complete description of a spin
1/2
particle
.202
11.3.1
Observables
.203
11.4
Physical spin effects
.204
11
.õ
Spin magnetic moment
.205
11.5.1
Hamiltonian of a one-electron atom
.205
11.6
The Stern- Gerlach experiment
.206
11.6.1
Principle of the experiment
.206
11.6.2
Semi-classical analysis
.207
11.6.3
Experimental results
.208
11.6.4
Explanation of the Stern-Gerlach experiment
.208
11.6.5
Successive Stern Gerlach setups
.211
11.6.6
Measurement, along' an arbitrary axis
.211
1.1.7
The discovery of spin
.213
11.7.1
The hidden sides of the Stern-Gerlach experiment
.213
11.7.2
Einstein and
Ehrenfest
"s objections
.215
11.7-.3 Anomalous
Zeeman
effect
.216
11.7.4
Bohr's challenge to
Pauli.217
11.7.5
The spin hypothesis
.217
11.7.6
The fine structure of atomic lines
.218
11.8
Magnetism, magnetic resonance
.219
11.8.1
Spin effects, Larmor precession
.220
11.8.2
Larmor precession in a fixed magnetic field
.221
11.8.3
Rabrs calculation and experiment
.221
11.8.4
Nuclear magnetic resonance
.225
11.8.5
Magnetic moments of elementary particles
.227
11.9
Entertainment: Rotation by
2тг
of a spin
1/2.228
12
The
Pauli
Principle
.229
12.1
Indistinguishability of two identical particles
.230
12.1.1
Identical particles in classical physics
.230
12.1.2
The quantum problem
.230
12.1.3
Example of ambiguities
.231
12.2
Systems of two spin
1/2
particles, total spin
.232
12.2.1
The Hubert space of the problem
.232
12.2.2
Hubert space of spin variables
.232
1.2.2.3
Matrix representation
.233
12.2.4
Total spin states
.233
12.3
Two-particle system; the exchange operator
.235
12.3.1
The Hubert space1 for the two-particle .system
.235
12.3.2
The exchange operator between identical particles
.236
Contents xiii
12.3.3
Symmetry of the states
.237
12.4
The
Pauli
principle
.238
12.4.1
The case of two particles
.238
12.4.2
Independent
fermions
and exclusion principle
.239
12.4.3
The case of
N
identical particles
.239
12.5
Physical consequences of the
Pauli
principle
.241
12.5.1
Exchange force between two
fermions
.241
12.5.2
The ground state of
N
identical independent particles.
. 241
12.5.3
Behavior of fermion and boson systems at
low7 temperatures
.243
13
Entangled states: The way of paradoxes
.247
13.1
The EPR paradox
.247
13.2
The version of David
Bohm
.249
13.2.1
Bell's inequality
.251
13.2.2
Experimental tests
.254
13.3
Quantum cryptography: how to enjoy a nuisance
.256
13.3.1
The communication between Alice and Bob
.256
13.3.2
Present experimental setups
.258
13.4
Quantum
teleportat
ion
.260
13.4.1
Bell states
.260
13.4.2
Teleportation
.261
14
Quantum mechanics in the Universe
.263
14.1
Quantum mechanics and astronomy
.265
14.1.1
Life and death of stars
.265
14.1.2
Spectroscopy
.268
14.2
Radioastronoiny, the interstellar medium
.268
14.2.1
The interstellar medium
.269
14.3
Cosmic background radiation: Birth of the Universe
.273
14.4
The 21-cm line of hydrogen
.275
14.4.1
Hyperfine structure of hydrogen
.276
14.4.2
Hydrogen
maser
.278
14.4.3
Importance of the 21-cm Hue
.279
14.5
The Milky Way
.280
14.6
The intergalactic medium: star wars
.281
14.6.1
Spiral arms, birthplaces of stars
.285
14.7
Interstellar molecules, the origin of life
.287
14.7.1
Rotation spectra of' molecules
.287
14.7.2
Interstellar molecules
.288
14.7.3
The origin of life
.289
14.8
Where are they? Quantum mechanics, the tmiversal
cosmic language
.291
14.8.1
Life, intelligence, and thought
.291
14.8.2
Listening to extraterrestrials
.293
xiv Contents
14.8.3
Quantum mechanics, the universal cosmic language
. 295
Index
.3Ü3 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Basdevant, Jean-Louis 1939- |
| author_GND | (DE-588)133559130 |
| author_facet | Basdevant, Jean-Louis 1939- |
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| author_sort | Basdevant, Jean-Louis 1939- |
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| bvnumber | BV022872159 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.125 |
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| callnumber-sort | QC 3174.125 |
| callnumber-subject | QC - Physics |
| classification_rvk | UK 1000 |
| ctrlnum | (OCoLC)123410782 (DE-599)BVBBV022872159 |
| 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 |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV022872159 |
| illustrated | Illustrated |
| index_date | 2024-07-02T18:47:38Z |
| indexdate | 2024-07-09T21:07:25Z |
| institution | BVB |
| isbn | 0387377425 9780387377421 0387377441 9780387377445 |
| language | English |
| lccn | 2006936625 |
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| physical | XVI, 307 S. Ill. 24 cm |
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| spelling | Basdevant, Jean-Louis 1939- Verfasser (DE-588)133559130 aut Lectures on quantum mechanics Jean-Louis Basdevant New York Springer 2007 XVI, 307 S. Ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index 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 Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016077239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Basdevant, Jean-Louis 1939- Lectures on quantum mechanics Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4123623-3 |
| title | Lectures on quantum mechanics |
| title_auth | Lectures on quantum mechanics |
| title_exact_search | Lectures on quantum mechanics |
| title_exact_search_txtP | Lectures on quantum mechanics |
| title_full | Lectures on quantum mechanics Jean-Louis Basdevant |
| title_fullStr | Lectures on quantum mechanics Jean-Louis Basdevant |
| title_full_unstemmed | Lectures on quantum mechanics Jean-Louis Basdevant |
| title_short | Lectures on quantum mechanics |
| title_sort | lectures on quantum mechanics |
| 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=016077239&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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