Quantum mechanics: a modern and concise introductory course
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2007
|
| Edition: | 2., rev. ed. |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 229 - 232 |
| Physical Description: | XIX, 239 S. Ill., graph. Darst. 24 cm |
| ISBN: | 9783540462156 3540462155 |
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| 100 | 1 | |a Bès, Daniel R. |d 1931- |e Verfasser |0 (DE-588)102583836X |4 aut | |
| 245 | 1 | 0 | |a Quantum mechanics |b a modern and concise introductory course |c Daniel R. Bes |
| 250 | |a 2., rev. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XIX, 239 S. |b Ill., graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 229 - 232 | ||
| 650 | 7 | |a Mecânica quântica |2 larpcal | |
| 650 | 4 | |a Théorie quantique | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory | |
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| _version_ | 1805089660042477568 |
|---|---|
| adam_text |
Contents
1
Introduction
. 1
2
Principles of Quantum Mechanics
. 5
2.1
Classical Physics
. 5
2.2*
Mathematical Framework of Quantum Mechanics
. 6
2.3
Basic Principles of Quantum Mechanics
. 9
2.3.1
Some Comments on the Basic Principles
. 11
2.4
Measurement Process
. 12
2.4.1
The Concept of Measurement
. 12
2.4.2
Quantum Measurements
. 13
2.5
Some Consequences of the Basic Principles
. 15
2.6
Commutation Relations and the Uncertainty Principle
. 19
2.7*
Hubert Spaces and Operators
. 21
2.7.1*
Some Properties of Hermitian Operators
. 23
2.7.2*
Unitary Transformations
. 24
2.8*
Notions of Probability Theory
. 25
Problems
. 26
3
The
Heisenberg
Realization of Quantum Mechanics
. 29
3.1
Matrix Formalism
. 29
3.1.1
A Realization of the Hubert Space
. 29
3.1.2
The Solution of the Eigenvalue Equation
. 31
3.1.3
Application to
2x2
Matrices
. 32
3.2
Harmonic Oscillator
. 34
3.2.1
Solution of the Eigenvalue Equation
. 35
3.2.2
Some Properties of the Solution
. 37
Problems
. 39
4
The
Schrödinger
Realization of Quantum Mechanics
. 43
4.1
Time-Independent
Schrödinger
Equation
. 43
4.1.1
Probabilistic Interpretation of Wave Functions
. 45
XVI Contents
4.2
The Harmonic Oscillator Revisited
. 47
4.2.1
Solution of the
Schrödinger
Equation
. 47
4.2.2
Spatial Features of the Solutions
. 49
4.3
Free Particle
. 51
4.4
One-Dimensional Bound Problems
. 53
4.4.1
Infinite Square Well Potential. Electron Gas
. 53
4.4.2
Finite Square Well Potential
. 55
4.5
One-Dimensional Unbound Problems
. 56
4.5.1
One-Step Potential
. 57
4.5.2
Square Barrier
. 59
4.5.3
Scanning Tunneling Microscope
. 61
4.6Í
Band Structure of Crystals
. 62
4.6.1t
Region
1:
-Vq
<
-E
< -Vi . 63
4.6.2t Region II:
-Vi <
-E
< 0. 64
Problems
. 65
5
Angular Momenta
. 67
5.1
Eigenvalues and Eigenstates
. 67
5.1.1
Matrix Treatment
. 67
5.1.2
Treatment Using Position Wave Functions
. 69
5.2
Spin
. 71
5.2.1
Stern-Gerlach Experiment
. 71
5.2.2
Spin Formalism
. 73
5.3
Addition of Angular Momenta
. 75
5.4*
Details of Matrix Treatment
. 77
5.5*
Details of the Treatment of Orbital Angular Momentum
. 78
5.5.1*
Eigenvalue Equation for the Operator Lz
. 78
5.5.2*
Eigenvalue Equation for the Operators
L2, Ĺz
. 78
5.6*
Coupling with Spin
s
= 1/2. 80
Problems
. 80
6
Three-Dimensional Hamiltonian Problems
. 83
6.1
Central Potentials
. 83
6.1.1
Coulomb and Harmonic Oscillator Potentials
. 84
6.2
Spin-Orbit Interaction
. 86
6.3
Some Elements of Scattering Theory
. 88
6.3.1
Boundary Conditions
. 88
6.3.2
Expansion in Partial Waves
. 89
6.3.3
Cross-Sections
. 89
6.4*
Solutions to the Coulomb and Oscillator Potentials
. 91
6.5*
Some Properties of Spherical Bessel Functions
. 94
Problems
. . 95
Contents XVII
Many-Body Problems
. 99
7.1
The
Pauli
Principle
.100
7.2
Two-Electron Problems
.103
7.3
Periodic Tables
.104
7.4
Motion of Electrons in Solids
.108
7.4.1
Electron Gas
.108
7.4.2t Band Structure of Crystals
.110
7.4.3t Phonons
in Lattice Structures
.110
7.4.4t Quantum Dots
.113
7.5*
Bose-Einstein Condensation
.115
7.6*
Quantum Hall Effects
.117
7.6.1*
Integer Quantum Hall Effect
.118
7.6.2*
Fractional Quantum Hall Effect
.121
7.7*
Quantum Statistics
.122
7.8*
Occupation Number Representation
(Second Quantization)
.124
Problems
.126
Approximate Solutions to Quantum Problems
.129
8.1
Perturbation Theory
.129
8.2
Variational Procedure
.132
8.3
Ground State of the He Atom
.132
8.4
Molecules
.133
8.4.1
Intrinsic Motion. Covalent Binding
.133
8.4.2
Vibrational and Rotational Motions
.135
8.4.3
Characteristic Energies
.137
8.5
Approximate Matrix Diagonalizations
.138
8.5.1*
Approximate Treatment of Periodic Potentials
.139
8.6*
Matrix Elements
Involving the Inverse of the Interparticle Distance
.140
8.7*
Quantization with Constraints
.141
8.7.1*
Constraints
.142
8.7.2*
Outline of the
BRST
Solution
.143
Problems
.144
Time-Dependence in Quantum Mechanics
.147
9.1
The Time Principle
.147
9.2
Time-Dependence of Spin States
.149
9.2.1
Larmor Precession
.149
9.2.2
Magnetic Resonance
.150
9.3
Sudden Change in the Hamiltonian
.152
9.4
Time-Dependent Perturbation Theory
.152
9.4.1
Transition Amplitudes and Probabilities
.153
XVIII
Contents
9.4.2
Constaiit-in-Time
Perturbation
.153
9.4.3
Mean Lifetime and Energy-Time
Uncertainty Relation
.155
9.5ł
Quantum Electrodynamics for Newcomers
.156
9.5.
lł
Classical Description of the Radiation Field
.156
9.5.2t Quantization of the Radiation Field
.157
9.5.ЗЇ
Interaction of Light with Particles
.159
9.5.4Í
Emission and Absorption of Radiation
.160
9.5.5t Selection Rules
.161
Э.б.б1'
Lasers and
Masers.162
Problems
.163
10
Entanglement and Quantum Information
.167
10.1
Conceptual Framework
.167
10.2
Entanglement
.168
10.2.1
The Bell States
.170
10.3ł
No-Cloning Theorem
.171
10.4
Quantum Cryptography
.171
10.5
Teleportation
.172
10.6t
Quantum Computation
.174
10.6.1f Factorization
.174
lO.1^ Quantum Gates
.177
10.7.1+
One-Qubit Systems
.177
10.7.2t Two-Qubit
Systems
.178
10.7.3t n-Qubit
Systems
.179
Problems
.180
11
Experimental Tests of Quantum Mechanics
.183
11.1
Two-Slit Experiments
.183
11.2
EPR and Bell Inequalities
.187
12
Measurements and Alternative Interpretations
of Quantum Mechanics. Decoherence
.191
12.1
Measurements and Alternative Interpretations
of Quantum Mechanics
.191
12.1.1
Measurements and the Copenhagen
Interpretation
.191
12.1.2t
Two Alternative Interpretations
.193
12.2t Decoherence
.194
12.3t
The Density Matrix
.196
12.3.lt Application to Decoherence
.198
Problems
.199
Contents XIX
13
A Brief History of Quantum Mechanics
.201
13.1
Social Context in Central Europe During the
1920s .201
13.2
Prehistory of Quantum Physics
(1860
<t<
1900).203
13.3
Old Quantum Theory
(1900 <
t
< 1925).204
13.3.1
Radiation
.204
13.3.2
Matter
.205
13.4
Quantum Mechanics
(1925 <
í
< 1928).207
13.5
Philosophical Aspects
.210
13.5.1
Complementarity Principle
.210
13.5.2
Discussions between Bohr and Einstein
.211
13.6
Recent History
.214
14
Solutions to Problems and Physical Constants
.215
14.1
Solutions to Problems
.215
14.2
Physical Units and Constants
.227
References
.229
Index
.233 |
| adam_txt |
Contents
1
Introduction
. 1
2
Principles of Quantum Mechanics
. 5
2.1
Classical Physics
. 5
2.2*
Mathematical Framework of Quantum Mechanics
. 6
2.3
Basic Principles of Quantum Mechanics
. 9
2.3.1
Some Comments on the Basic Principles
. 11
2.4
Measurement Process
. 12
2.4.1
The Concept of Measurement
. 12
2.4.2
Quantum Measurements
. 13
2.5
Some Consequences of the Basic Principles
. 15
2.6
Commutation Relations and the Uncertainty Principle
. 19
2.7*
Hubert Spaces and Operators
. 21
2.7.1*
Some Properties of Hermitian Operators
. 23
2.7.2*
Unitary Transformations
. 24
2.8*
Notions of Probability Theory
. 25
Problems
. 26
3
The
Heisenberg
Realization of Quantum Mechanics
. 29
3.1
Matrix Formalism
. 29
3.1.1
A Realization of the Hubert Space
. 29
3.1.2
The Solution of the Eigenvalue Equation
. 31
3.1.3
Application to
2x2
Matrices
. 32
3.2
Harmonic Oscillator
. 34
3.2.1
Solution of the Eigenvalue Equation
. 35
3.2.2
Some Properties of the Solution
. 37
Problems
. 39
4
The
Schrödinger
Realization of Quantum Mechanics
. 43
4.1
Time-Independent
Schrödinger
Equation
. 43
4.1.1
Probabilistic Interpretation of Wave Functions
. 45
XVI Contents
4.2
The Harmonic Oscillator Revisited
. 47
4.2.1
Solution of the
Schrödinger
Equation
. 47
4.2.2
Spatial Features of the Solutions
. 49
4.3
Free Particle
. 51
4.4
One-Dimensional Bound Problems
. 53
4.4.1
Infinite Square Well Potential. Electron Gas
. 53
4.4.2
Finite Square Well Potential
. 55
4.5
One-Dimensional Unbound Problems
. 56
4.5.1
One-Step Potential
. 57
4.5.2
Square Barrier
. 59
4.5.3
Scanning Tunneling Microscope
. 61
4.6Í
Band Structure of Crystals
. 62
4.6.1t
Region
1:
-Vq
<
-E
< -Vi . 63
4.6.2t Region II:
-Vi <
-E
< 0. 64
Problems
. 65
5
Angular Momenta
. 67
5.1
Eigenvalues and Eigenstates
. 67
5.1.1
Matrix Treatment
. 67
5.1.2
Treatment Using Position Wave Functions
. 69
5.2
Spin
. 71
5.2.1
Stern-Gerlach Experiment
. 71
5.2.2
Spin Formalism
. 73
5.3
Addition of Angular Momenta
. 75
5.4*
Details of Matrix Treatment
. 77
5.5*
Details of the Treatment of Orbital Angular Momentum
. 78
5.5.1*
Eigenvalue Equation for the Operator Lz
. 78
5.5.2*
Eigenvalue Equation for the Operators
L2, Ĺz
. 78
5.6*
Coupling with Spin
s
= 1/2. 80
Problems
. 80
6
Three-Dimensional Hamiltonian Problems
. 83
6.1
Central Potentials
. 83
6.1.1
Coulomb and Harmonic Oscillator Potentials
. 84
6.2
Spin-Orbit Interaction
. 86
6.3
Some Elements of Scattering Theory
. 88
6.3.1
Boundary Conditions
. 88
6.3.2
Expansion in Partial Waves
. 89
6.3.3
Cross-Sections
. 89
6.4*
Solutions to the Coulomb and Oscillator Potentials
. 91
6.5*
Some Properties of Spherical Bessel Functions
. 94
Problems
. . 95
Contents XVII
Many-Body Problems
. 99
7.1
The
Pauli
Principle
.100
7.2
Two-Electron Problems
.103
7.3
Periodic Tables
.104
7.4
Motion of Electrons in Solids
.108
7.4.1
Electron Gas
.108
7.4.2t Band Structure of Crystals
.110
7.4.3t Phonons
in Lattice Structures
.110
7.4.4t Quantum Dots
.113
7.5*
Bose-Einstein Condensation
.115
7.6*
Quantum Hall Effects
.117
7.6.1*
Integer Quantum Hall Effect
.118
7.6.2*
Fractional Quantum Hall Effect
.121
7.7*
Quantum Statistics
.122
7.8*
Occupation Number Representation
(Second Quantization)
.124
Problems
.126
Approximate Solutions to Quantum Problems
.129
8.1
Perturbation Theory
.129
8.2
Variational Procedure
.132
8.3
Ground State of the He Atom
.132
8.4
Molecules
.133
8.4.1
Intrinsic Motion. Covalent Binding
.133
8.4.2
Vibrational and Rotational Motions
.135
8.4.3
Characteristic Energies
.137
8.5
Approximate Matrix Diagonalizations
.138
8.5.1*
Approximate Treatment of Periodic Potentials
.139
8.6*
Matrix Elements
Involving the Inverse of the Interparticle Distance
.140
8.7*
Quantization with Constraints
.141
8.7.1*
Constraints
.142
8.7.2*
Outline of the
BRST
Solution
.143
Problems
.144
Time-Dependence in Quantum Mechanics
.147
9.1
The Time Principle
.147
9.2
Time-Dependence of Spin States
.149
9.2.1
Larmor Precession
.149
9.2.2
Magnetic Resonance
.150
9.3
Sudden Change in the Hamiltonian
.152
9.4
Time-Dependent Perturbation Theory
.152
9.4.1
Transition Amplitudes and Probabilities
.153
XVIII
Contents
9.4.2
Constaiit-in-Time
Perturbation
.153
9.4.3
Mean Lifetime and Energy-Time
Uncertainty Relation
.155
9.5ł
Quantum Electrodynamics for Newcomers
.156
9.5.
lł
Classical Description of the Radiation Field
.156
9.5.2t Quantization of the Radiation Field
.157
9.5.ЗЇ
Interaction of Light with Particles
.159
9.5.4Í
Emission and Absorption of Radiation
.160
9.5.5t Selection Rules
.161
Э.б.б1'
Lasers and
Masers.162
Problems
.163
10
Entanglement and Quantum Information
.167
10.1
Conceptual Framework
.167
10.2
Entanglement
.168
10.2.1
The Bell States
.170
10.3ł
No-Cloning Theorem
.171
10.4
Quantum Cryptography
.171
10.5
Teleportation
.172
10.6t
Quantum Computation
.174
10.6.1f Factorization
.174
lO.1^ Quantum Gates
.177
10.7.1+
One-Qubit Systems
.177
10.7.2t Two-Qubit
Systems
.178
10.7.3t n-Qubit
Systems
.179
Problems
.180
11
Experimental Tests of Quantum Mechanics
.183
11.1
Two-Slit Experiments
.183
11.2
EPR and Bell Inequalities
.187
12
Measurements and Alternative Interpretations
of Quantum Mechanics. Decoherence
.191
12.1
Measurements and Alternative Interpretations
of Quantum Mechanics
.191
12.1.1
Measurements and the Copenhagen
Interpretation
.191
12.1.2t
Two Alternative Interpretations
.193
12.2t Decoherence
.194
12.3t
The Density Matrix
.196
12.3.lt Application to Decoherence
.198
Problems
.199
Contents XIX
13
A Brief History of Quantum Mechanics
.201
13.1
Social Context in Central Europe During the
1920s .201
13.2
Prehistory of Quantum Physics
(1860
<t<
1900).203
13.3
Old Quantum Theory
(1900 <
t
< 1925).204
13.3.1
Radiation
.204
13.3.2
Matter
.205
13.4
Quantum Mechanics
(1925 <
í
< 1928).207
13.5
Philosophical Aspects
.210
13.5.1
Complementarity Principle
.210
13.5.2
Discussions between Bohr and Einstein
.211
13.6
Recent History
.214
14
Solutions to Problems and Physical Constants
.215
14.1
Solutions to Problems
.215
14.2
Physical Units and Constants
.227
References
.229
Index
.233 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bès, Daniel R. 1931- |
| author_GND | (DE-588)102583836X |
| author_facet | Bès, Daniel R. 1931- |
| author_role | aut |
| author_sort | Bès, Daniel R. 1931- |
| author_variant | d r b dr drb |
| building | Verbundindex |
| bvnumber | BV023013903 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.45 |
| callnumber-search | QC174.45 |
| callnumber-sort | QC 3174.45 |
| callnumber-subject | QC - Physics |
| classification_rvk | UK 1000 |
| ctrlnum | (OCoLC)75927465 (DE-599)DNB981013163 |
| 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 | 2., rev. ed. |
| format | Book |
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| id | DE-604.BV023013903 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:10:28Z |
| indexdate | 2024-07-20T09:27:26Z |
| institution | BVB |
| isbn | 9783540462156 3540462155 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016218089 |
| oclc_num | 75927465 |
| open_access_boolean | |
| owner | DE-703 DE-634 DE-11 DE-355 DE-BY-UBR |
| owner_facet | DE-703 DE-634 DE-11 DE-355 DE-BY-UBR |
| physical | XIX, 239 S. Ill., graph. Darst. 24 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| spelling | Bès, Daniel R. 1931- Verfasser (DE-588)102583836X aut Quantum mechanics a modern and concise introductory course Daniel R. Bes 2., rev. ed. Berlin [u.a.] Springer 2007 XIX, 239 S. Ill., graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 229 - 232 Mecânica quântica larpcal Théorie quantique Quantentheorie Quantum theory 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=2848974&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016218089&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bès, Daniel R. 1931- Quantum mechanics a modern and concise introductory course Mecânica quântica larpcal Théorie quantique Quantentheorie Quantum theory 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_exact_search_txtP | Quantum mechanics a modern and concise introductory course |
| title_full | Quantum mechanics a modern and concise introductory course Daniel R. Bes |
| title_fullStr | Quantum mechanics a modern and concise introductory course Daniel R. Bes |
| title_full_unstemmed | Quantum mechanics a modern and concise introductory course Daniel R. Bes |
| title_short | Quantum mechanics |
| title_sort | quantum mechanics a modern and concise introductory course |
| title_sub | a modern and concise introductory course |
| topic | Mecânica quântica larpcal Théorie quantique Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Mecânica quântica Théorie quantique Quantentheorie Quantum theory Quantenmechanik |
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