Introduction to quantum mechanics: a time-dependent perspective
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| Format: | Buch |
| Sprache: | English |
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Sausalito, Calif.
Univ. Science Books
2007
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXIV, 662 S. Ill., graph. Darst. |
| ISBN: | 1891389238 9781891389238 9781891389993 |
Internformat
MARC
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| 100 | 1 | |a Tannor, David J. |d 1958- |e Verfasser |0 (DE-588)142854689 |4 aut | |
| 245 | 1 | 0 | |a Introduction to quantum mechanics |b a time-dependent perspective |c David J. Tannor |
| 264 | 1 | |a Sausalito, Calif. |b Univ. Science Books |c 2007 | |
| 300 | |a XXIV, 662 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Quantenmechanik - Zeitabhängigkeit | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum theory | |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zeitabhängigkeit |0 (DE-588)4320088-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804134597417500672 |
|---|---|
| adam_text | Contents
Foreword
xiii
Preface
xv
Structure of the Book and Teacher s Guide
xix
PART I
Pictures and Concepts
I
chapter I The Time-Dependent
Schrödinger
Equation
3
1.1
Separation of Variables and
Reconstitution
of the Wavepacket
4
1.2
Expectation Values
5
1.3
A Worked Example: Particle in Half a Box
7
Further Reading and Historical Notes
10
References
11
chapter
2
The Free-Particle Wavepacket
13
2.1
General Solution
13
2.2
The Center of the Wavepacket
16
2.3
The Dispersion of the Wavepacket
18
Problems
20
Further Reading and Historical Notes
21
References
21
chapter
3
The Gaussian Wavepacket
23
3.1
The Gaussian Free Particle
23
3.2
General Properties of Gaussian Wavepackets
26
3.3
Gaussian in a Quadratic Potential
28
3.4
Reexamination of the Stationary Phase Method
31
Problems
33
References
34
chapter
4
Correspondence between Classical and Quantum Dynamics
35
4.1
Ehrenfest s Theorem
35
4.2
Bohmian Mechanics and the Classical Limit
38
4.3
Fractional Revivals
46
Problems
49
References
53
VII
VÜi Contents
chapter
5
The Wigner Representation and the Density Operator
55
5.1
The Concept of Phase Space
56
5.2
The Wigner Representation of Wavepackets
58
5.3
The Density Operator
61
5.4
Wigner Representation of the Density Operator
68
Problems
74
References
76
chapter
6
Correlation Functions and Spectra
81
6.1
Spectra as Fourier Transforms of Wavepacket Correlation Functions
81
6.2
General Properties of Fourier Transforms
86
6.3
Eigenfunctions as Fourier Transforms of Wavepackets
97
Problems
103
References
108
chapter
7
One-Dimensional Barrier Scattering
109
7.1
Wavepacket Formulation of Reflection and Transmission
Coefficients
110
7.2
Cross-Correlation Function Formulation of Barrier Scattering and the
^-Matrix
116
7.3
Scattering Theory Using Eigenstates
122
7.4
Overlap Integrals of Scattering Eigenstates
128
7.5
Reconstituting the Wavepacket from the Scattering Eigenstates
132
7.6
Resonances and Time Delay
134
Problems
138
References
140
part II Formal Theory and Methods of Approximation HI
chapter
8
Linear Algebra and Quantum Mechanics
143
8.1
Linear Vector Spaces
143
8.2
Operators: Mapping a Wavefunction to Another Wavefunction
147
8.3
Discrete Basis Sets: The Bridge between Operators-Wavefunctions
Ф=Ф
Matrices-Vectors
159
8.4
Continuous Basis Sets
172
Problems
179
References
183
chapter
9
Approximate Solutions of the Time-Dependent
Schrödinger
Equation
185
9.1
The
Schrödinger, Heisenberg
and Interaction Pictures
186
9.2
Time-Dependent Perturbation Theory
190
9.3
The Magnus Expansion and Wei-Norman Factorization
193
9.4
Adiabatic Dynamics and the Geometrical Phase
199
Contents
9.5
Periodic Hamiltonians
and Floquet Theory
208
9.6 Variational
Principles and the Time-Dependent Self-Consistent Field
Approximation
214
Problems
220
References
222
chapter
10
Path Integration, the van Vleck Propagator and
Semiclassical Mechanics
227
10.1
The Classical Action
228
10.2
Path Integration
238
10.3
The van Vleck Propagator
240
10.4
The Propagator as a Unitary Transformation
246
10.5
Gaussian Wavepackets and the van Vleck Propagator
257
References
268
chapter I I Numerical Methods for Solving the Time-Dependent
Schrödinger
Equation
273
11.1
Spectral Projection and Collocation
275
11.2
The
Pseudospectral
Basis
281
11.3
Gaussian Quadrature
285
11.4
Representation of the Hamiltonian in the Reduced Space
293
11.5
The Discrete Variable Representation
297
11.6
The Fourier Method
301
11.7
Time Propagation
312
Problems
326
References
329
IX
part III Applications
333
chapter
12
Introduction to Molecular Dynamics
335
12.1
The Born-Oppenheimer Approximation
335
12.2
Adiabatic versus Diabatic Representations
338
12.3
Potential Energy Surfaces
345
12.4
Normal Modes of Vibration
352
12.5
Chemical Reactions and Transition State Theory
356
12.6
Symmetry and Permutations
370
12.7
Hyperspherical Coordinates
382
History and Further Reading
387
Problems
388
References
390
chapter
13
Femtosecond Pulse Pair Excitation
395
13.1
First-Order Processes: Wavepacket
Interferometry
395
13.2
Second-Order Processes: Clocking Chemical Reactions
403
Contents
13.3
Coherent Nonlinear Spectroscopy
408
13.4
Density Operator Formulation of Optical Perturbations
419
References
424
chapter
14
One-and Two-Photon Electronic Spectroscopy
427
14.1
Electronic Absorption and Emission Spectroscopy
433
14.2
Transition State Spectroscopy
445
14.3
Resonance Raman Spectroscopy
449
14.4
Dispersed Fluorescence Spectroscopy
465
Problems
473
References
475
chapter
15
Strong Field Excitation
479
15.1
Two-Level System
479
15.2
The Feynman-Vernon-Hellwarth (FVH) Representation
482
15.3
Dressed States
486
15.4
Adiabatic Excitation with Strong Fields
490
15.5
Impulsive Excitation
499
15.6
Optical Paralysis
501
Problems
504
References
505
chapter
16
Design of Femtosecond Pulse Sequences to Control
Chemical Reactions
509
16.1
Intuitive Control Concepts
511
16.2
Variational Formulation of Control of Product Formation
516
16.3
Applications of the Variational Formulation
528
16.4
Multiple Pathway Interference
534
16.5
Chirped Pulse Excitation
539
16.6
Learning Algorithms
544
Problems
547
References
553
chapter
17
Wavepacket Approach to
Photodissociation
559
17.1
Introduction
559
17.2
The Eigenstates of an Asymptotic Hamiltonian
560
17.3
The Eigenstates of a Scattering Hamiltonian
561
17.4
M0ller Operators
566
17.5
Wavepacket Formulation of
Photodissociation
569
17.6
Applications
571
References
577
chapter
18
Wavepacket Correlation Function Formulation
of Reactive Scattering
579
18.1
The Concept of an Arrangement Channel and the Problem of
Coordinate Systems
580
Contents
18.2
The Eigenstates of a Scattering Hamiltonian with Multiple Arrangement
Channels
581
18.3
Wavepacket Cross-Correlation Function Formulation of
Sßa(E) 586
18.4
Application to
Collinear
H
+
H2
->■
H2
+
H
591
18.5
Cumulative
Reaction Probability
594
References
600
appendix A The Dirac Delta Function and the Cauchy Principal Value
603
A.I The Dirac Delta Function
603
A.2 The Cauchy Principal Value
605
References
608
appendix
В
Composite Systems
609
B.I Wavefunction of a Composite System: Separability and
Entanglement
609
B.2 Density Matrix of a Composite System
610
B.3 Reduced Density Matrix
611
В
.4
Purity of the Reduced Density Matrix
613
References
615
appendix
С
Normalization and Orthogonality of Scattering Eigenstates
6
1
7
C.I Single Step
617
C.2 Concatenation of Steps
620
Problems
620
References
621
appendix
D
Units and Conversions
623
D.
1
Energy Conversions and Time Scales
623
D.2 Units of Electric Field Amplitude and Intensity
624
xi
Index
625
|
| adam_txt |
Contents
Foreword
xiii
Preface
xv
Structure of the Book and Teacher's Guide
xix
PART I
Pictures and Concepts
I
chapter I The Time-Dependent
Schrödinger
Equation
3
1.1
Separation of Variables and
Reconstitution
of the Wavepacket
4
1.2
Expectation Values
5
1.3
A Worked Example: Particle in Half a Box
7
Further Reading and Historical Notes
10
References
11
chapter
2
The Free-Particle Wavepacket
13
2.1
General Solution
13
2.2
The Center of the Wavepacket
16
2.3
The Dispersion of the Wavepacket
18
Problems
20
Further Reading and Historical Notes
21
References
21
chapter
3
The Gaussian Wavepacket
23
3.1
The Gaussian Free Particle
23
3.2
General Properties of Gaussian Wavepackets
26
3.3
Gaussian in a Quadratic Potential
28
3.4
Reexamination of the Stationary Phase Method
31
Problems
33
References
34
chapter
4
Correspondence between Classical and Quantum Dynamics
35
4.1
Ehrenfest's Theorem
35
4.2
Bohmian Mechanics and the Classical Limit
38
4.3
Fractional Revivals
46
Problems
49
References
53
VII
VÜi Contents
chapter
5
The Wigner Representation and the Density Operator
55
5.1
The Concept of Phase Space
56
5.2
The Wigner Representation of Wavepackets
58
5.3
The Density Operator
61
5.4
Wigner Representation of the Density Operator
68
Problems
74
References
76
chapter
6
Correlation Functions and Spectra
81
6.1
Spectra as Fourier Transforms of Wavepacket Correlation Functions
81
6.2
General Properties of Fourier Transforms
86
6.3
Eigenfunctions as Fourier Transforms of Wavepackets
97
Problems
103
References
108
chapter
7
One-Dimensional Barrier Scattering
109
7.1
Wavepacket Formulation of Reflection and Transmission
Coefficients
110
7.2
Cross-Correlation Function Formulation of Barrier Scattering and the
^-Matrix
116
7.3
Scattering Theory Using Eigenstates
122
7.4
Overlap Integrals of Scattering Eigenstates
128
7.5
Reconstituting the Wavepacket from the Scattering Eigenstates
132
7.6
Resonances and Time Delay
134
Problems
138
References
140
part II Formal Theory and Methods of Approximation HI
chapter
8
Linear Algebra and Quantum Mechanics
143
8.1
Linear Vector Spaces
143
8.2
Operators: Mapping a Wavefunction to Another Wavefunction
147
8.3
Discrete Basis Sets: The Bridge between Operators-Wavefunctions
Ф=Ф
Matrices-Vectors
159
8.4
Continuous Basis Sets
172
Problems
179
References
183
chapter
9
Approximate Solutions of the Time-Dependent
Schrödinger
Equation
185
9.1
The
Schrödinger, Heisenberg
and Interaction Pictures
186
9.2
Time-Dependent Perturbation Theory
190
9.3
The Magnus Expansion and Wei-Norman Factorization
193
9.4
Adiabatic Dynamics and the Geometrical Phase
199
Contents
9.5
Periodic Hamiltonians
and Floquet Theory
208
9.6 Variational
Principles and the Time-Dependent Self-Consistent Field
Approximation
214
Problems
220
References
222
chapter
10
Path Integration, the van Vleck Propagator and
Semiclassical Mechanics
227
10.1
The Classical Action
228
10.2
Path Integration
238
10.3
The van Vleck Propagator
240
10.4
The Propagator as a Unitary Transformation
246
10.5
Gaussian Wavepackets and the van Vleck Propagator
257
References
268
chapter I I Numerical Methods for Solving the Time-Dependent
Schrödinger
Equation
273
11.1
Spectral Projection and Collocation
275
11.2
The
Pseudospectral
Basis
281
11.3
Gaussian Quadrature
285
11.4
Representation of the Hamiltonian in the Reduced Space
293
11.5
The Discrete Variable Representation
297
11.6
The Fourier Method
301
11.7
Time Propagation
312
Problems
326
References
329
IX
part III Applications
333
chapter
12
Introduction to Molecular Dynamics
335
12.1
The Born-Oppenheimer Approximation
335
12.2
Adiabatic versus Diabatic Representations
338
12.3
Potential Energy Surfaces
345
12.4
Normal Modes of Vibration
352
12.5
Chemical Reactions and Transition State Theory
356
12.6
Symmetry and Permutations
370
12.7
Hyperspherical Coordinates
382
History' and Further Reading
387
Problems
388
References
390
chapter
13
Femtosecond Pulse Pair Excitation
395
13.1
First-Order Processes: Wavepacket
Interferometry
395
13.2
Second-Order Processes: Clocking Chemical Reactions
403
Contents
13.3
Coherent Nonlinear Spectroscopy
408
13.4
Density Operator Formulation of Optical Perturbations
419
References
424
chapter
14
One-and Two-Photon Electronic Spectroscopy
427
14.1
Electronic Absorption and Emission Spectroscopy
433
14.2
Transition State Spectroscopy
445
14.3
Resonance Raman Spectroscopy
449
14.4
Dispersed Fluorescence Spectroscopy
465
Problems
473
References
475
chapter
15
Strong Field Excitation
479
15.1
Two-Level System
479
15.2
The Feynman-Vernon-Hellwarth (FVH) Representation
482
15.3
Dressed States
486
15.4
Adiabatic Excitation with Strong Fields
490
15.5
Impulsive Excitation
499
15.6
Optical Paralysis
501
Problems
504
References
505
chapter
16
Design of Femtosecond Pulse Sequences to Control
Chemical Reactions
509
16.1
Intuitive Control Concepts
511
16.2
Variational Formulation of Control of Product Formation
516
16.3
Applications of the Variational Formulation
528
16.4
Multiple Pathway Interference
534
16.5
Chirped Pulse Excitation
539
16.6
Learning Algorithms
544
Problems
547
References
553
chapter
17
Wavepacket Approach to
Photodissociation
559
17.1
Introduction
559
17.2
The Eigenstates of an Asymptotic Hamiltonian
560
17.3
The Eigenstates of a Scattering Hamiltonian
561
17.4
M0ller Operators
566
17.5
Wavepacket Formulation of
Photodissociation
569
17.6
Applications
571
References
577
chapter
18
Wavepacket Correlation Function Formulation
of Reactive Scattering
579
18.1
The Concept of an Arrangement Channel and the Problem of
Coordinate Systems
580
Contents
18.2
The Eigenstates of a Scattering Hamiltonian with Multiple Arrangement
Channels
581
18.3
Wavepacket Cross-Correlation Function Formulation of
Sßa(E) 586
18.4
Application to
Collinear
H
+
H2
->■
H2
+
H
591
18.5
Cumulative
Reaction Probability
594
References
600
appendix A The Dirac Delta Function and the Cauchy Principal Value
603
A.I The Dirac Delta Function
603
A.2 The Cauchy Principal Value
605
References
608
appendix
В
Composite Systems
609
B.I Wavefunction of a Composite System: Separability and
Entanglement
609
B.2 Density Matrix of a Composite System
610
B.3 Reduced Density Matrix
611
В
.4
Purity of the Reduced Density Matrix
613
References
615
appendix
С
Normalization and Orthogonality of Scattering Eigenstates
6
1
7
C.I Single Step
617
C.2 Concatenation of Steps
620
Problems
620
References
621
appendix
D
Units and Conversions
623
D.
1
Energy Conversions and Time Scales
623
D.2 Units of Electric Field Amplitude and Intensity
624
xi
Index
625 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Tannor, David J. 1958- |
| author_GND | (DE-588)142854689 |
| author_facet | Tannor, David J. 1958- |
| author_role | aut |
| author_sort | Tannor, David J. 1958- |
| author_variant | d j t dj djt |
| building | Verbundindex |
| bvnumber | BV020871130 |
| 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 VE 5650 |
| classification_tum | PHY 020f |
| ctrlnum | (OCoLC)249110482 (DE-599)BVBBV020871130 |
| 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 | Chemie / Pharmazie Physik |
| discipline_str_mv | Chemie / Pharmazie Physik |
| format | Book |
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| id | DE-604.BV020871130 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:26:09Z |
| indexdate | 2024-07-09T20:27:08Z |
| institution | BVB |
| isbn | 1891389238 9781891389238 9781891389993 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014192872 |
| oclc_num | 249110482 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T DE-703 DE-188 DE-83 DE-384 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-29T DE-703 DE-188 DE-83 DE-384 |
| physical | XXIV, 662 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Univ. Science Books |
| record_format | marc |
| spelling | Tannor, David J. 1958- Verfasser (DE-588)142854689 aut Introduction to quantum mechanics a time-dependent perspective David J. Tannor Sausalito, Calif. Univ. Science Books 2007 XXIV, 662 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Quantenmechanik - Zeitabhängigkeit Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Zeitabhängigkeit (DE-588)4320088-6 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Zeitabhängigkeit (DE-588)4320088-6 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014192872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tannor, David J. 1958- Introduction to quantum mechanics a time-dependent perspective Quantenmechanik - Zeitabhängigkeit Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd Zeitabhängigkeit (DE-588)4320088-6 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4320088-6 |
| title | Introduction to quantum mechanics a time-dependent perspective |
| title_auth | Introduction to quantum mechanics a time-dependent perspective |
| title_exact_search | Introduction to quantum mechanics a time-dependent perspective |
| title_exact_search_txtP | Introduction to quantum mechanics a time-dependent perspective |
| title_full | Introduction to quantum mechanics a time-dependent perspective David J. Tannor |
| title_fullStr | Introduction to quantum mechanics a time-dependent perspective David J. Tannor |
| title_full_unstemmed | Introduction to quantum mechanics a time-dependent perspective David J. Tannor |
| title_short | Introduction to quantum mechanics |
| title_sort | introduction to quantum mechanics a time dependent perspective |
| title_sub | a time-dependent perspective |
| topic | Quantenmechanik - Zeitabhängigkeit Quantentheorie Quantum theory Quantenmechanik (DE-588)4047989-4 gnd Zeitabhängigkeit (DE-588)4320088-6 gnd |
| topic_facet | Quantenmechanik - Zeitabhängigkeit Quantentheorie Quantum theory Quantenmechanik Zeitabhängigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014192872&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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