Scattering theory: the quantum theory on nonrelativistic collisions
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| Format: | Book |
| Language: | English |
| Published: |
Mineola, NY
Dover Publ.
2006
|
| Edition: | Dover ed. |
| Series: | Dover books on engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | This Dover ed. is an unabridged republication of the revised ed. of the work, as publ. by Robert E. Krieger Publ. Comp., Malabar, Florida, in 1983. |
| Physical Description: | XVI, 477 S. graph. Darst. |
| ISBN: | 0486450139 9780486450131 |
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|---|---|
| adam_text | SCATTERING THEORY
The Quantum Theory of
Nonrelativistic Collisions
JOHN R TAYLOR
University of Colorado
DOVER PUBLICATIONS, INC
Mineola, New York
Contents
Introduction 1
1 Mathematical Preliminaries 6
1-a Hie Hilbert Space of State Vectors 7
1-b Subspaces 9
1-c Operators and Inverses 10
1-d Unitary Operators 13
1-e Isometric Operators 14
1-f Convergence of Vectors 16
1-g Operator Limits 19
2 The Scattering Operator for a Single Particle 21
2-a Classical Scattering 22
2-b Quantum Scattering 25
2-c The Asymptotic Condition 28
2-d Orthogonality and Asymptotic Completeness 31
2-e The Scattering Operator 34
2- f Unitarity 36
3 Cross Sections in Terms of the S Matrix 38
3- a Conservation of Energy 39
3-b The On-Shell T Matrix and Scattering Amplitude 42
3-c The Classical Cross Section 44
3-d Definition of the Quantum Cross Section 46
3-e Calculation of the Quantum Cross Section 49
3-f The Optical Theorem 53
xi
xii Contents
4 Scattering of Two Spinless Particles 56
4-a Two-Particle Wave Functions 57
4-b The Two-Particle S Operator 60
4-c Conservation of Energy-Momentum and the T Matrix 62
4-d Cross Sections in Various Frames 64
4- e The Center-of-Mass Cross Section 66
5 Scattering of Two Particles with Spin 69
5- a The Hilbert Space for Particles with Spin 70
5-b The S Operator for Particles with Spin 72
5-c The Amplitudes and Amplitude Matrix 73
5-d Sums and Averages Over Spins 76
5- e Hie In and Out Spinors 78
6 Invariance Principles and Conservation Laws 81
6- a Translational Invariance and Conservation of Momentum 82
6-b Rotational Invariance and Conservation of Angular Momentum 83
6-c The Partial-Wave Series for Spinless Particles 85
6-d Parity 90
6-e Time Reversal 91
6-f Invariance Principles for Particles with Spin;
Momentum-Space Analysis 95
6- g Invariance Principles for Particles with Spin;
Angular-Momentum Analysis 103
7 More About Particles with Spin 109
7- a Polarization and the Density Matrix 109
7-b The In and Out Density Matrices 113
7-c Polarization Experiments in (Spin K) — (Spin 0) Scattering 114
7-d The Helicity Formalism 119
7-e Some Useful Formulas 124
Contents xiii
8 The Green’s Operator and the T Operator 128
8-a The Green s Operator 129
8-b The T Operator 134
8- c Relation to the Midler Operators 135
M Relation to the Scattering Operator 138
9 The Bom Series 143
9- a The Born Series 144
9-b The Born Approximation 147
9-c The Yukawa Potential 150
N Scattering of Electrons off Atoms 153
9- e Interpretation of the Born Series in Terms of Feynman
Diagrams 157
10 The Stationary Scattering States 164
10- a Definition and Properties of the Stationary Scattering States 105
10-b Equations for the Stationary Scattering Vectors 168
10-c The Stationary Wave Functions 170
10- d A Spatial Description of the Scattering Process 173
11 The Partial-Wave Stationary States 180
11- a The Partial-Wave S Matrix 181
11-b The Free Radial Wave Functions 182
11-c The Partial-Wave Scattering States 185
11-d The Partial-Wave Lippmann-Schwinger Equation 188
11-e Properties of the Partial-Wave Amplitude 191
11-f The Regular Solution 197
11-g The Variable Phase Method 197
11-h Iterative Solution for the Regular Wave Function 201
11-i The Jost Function 204
11-j The Partial-Wave Born Series 207
Contents
xiv
12 Analytic Properties of the Partial-Wave
Amplitude 212
12-a Analytic Functions of a Complex Variable 213
12-b Analytic Properties of the Regular Solution 215
12-c Analytic Properties of the Jost Function and S Matrix 217
12-d Bound States and Poles of the S Matrix 223
12-e Levinson’s Theorem 226
12-f Threshold Behavior and Effective Range Formulas 229
12- g Zeros of the Jost Function at Threshold 232
13 Resonances 238
13- a Resonances and Poles of the S Matrix 240
13-b Bound States and Resonances 245
13-c Time Delay 249
13- d Decay of a Resonant State 253
14 Additional Topics in Single-Channel
Scattering 259
14- a Coulomb Scattering 259
14-b Coulomb Plus Short-Range Potentials 266
14-c The Distorted-Wave Born Approximation 270
14- d Variational Methods 273
14~e The K Matrix 280
15 Dispersion Relations and Complex Angular
Momenta 285
15- a Partial-Wave Dispersion Relations 287
15-b Forward Dispersion Relations 291
15-c Nonforward Dispersion Relations 294
15-d The Mandelstam Representation 297
15-e Complex Angular Momenta 302
15-f Regge Poles 306
15-g The Watson Transform 308
Contents xv
16 The Scattering Operator in Multichannel
Scattering 315
16-a Channels 316
16-b Channel Hamiltonians and Asymptotic States 321
16-c Orthogonality and Asymptotic Completeness 326
16-d A Little More Mathematics 331
16- e The Scattering Operator 334
17 Cross Sections and Invariance Principles in
Multichannel Scattering 338
17- a The Momentum-Space Basis Vectors 339
17-b Conservation of Energy and the On-Shell T Matrix 342
17-c Cross Sections 346
17-d Rotational Invariance 351
17- e Time-Reversal Invariance 353
18 Fundamentals of Time-Independent
Multichannel Scattering 358
18- a Hie Stationary Scattering States 359
18-b Hie Lippmann-Schwinger Equations 361
18-c The T Operators 363
18-d The Born Approximation; Elastic Scattering 364
18- e The Born Approximation; Excitation 367
19 Properties of the Multichannel Stationary
Wave Functions 372
19- a Asymptotic Form of the Stationary Wave Functions;
Collisions Without Rearrangement 373
19-b Asymptotic Form of the Stationary Wave Functions;
Rearrangement Collisions 378
19-c Expansion in Terms of Target States 380
19-d The Optical Potential 383
xvi
Contents
20 Analytic Properties and Multichannel
Resonances 391
20-a Analytic Properties 392
20-b Proof of Analytic Properties 396
20-c Bound States 405
20-d Resonances 407
20- e Decay of a Multichannel Resonance 413
21 Two More Topics in Multichannel Scattering 418
21- a The Distorted-Wave Born Approximation 418
21- b Final-State Interactions 424
22 Identical Particles 434
22- a The Formalism of Identical Particles 435
22-b Scattering of Two Identical Particles 441
22-c Multichannel Scattering with Identical Particles 448
22-d Transition Probabilities and Cross Sections 450
22-e Electron-Hydrogen Scattering 454
References 463
Index
|
| adam_txt |
SCATTERING THEORY
The Quantum Theory of
Nonrelativistic Collisions
JOHN R TAYLOR
University of Colorado
DOVER PUBLICATIONS, INC
Mineola, New York
Contents
Introduction 1
1 Mathematical Preliminaries 6
1-a Hie Hilbert Space of State Vectors 7
1-b Subspaces 9
1-c Operators and Inverses 10
1-d Unitary Operators 13
1-e Isometric Operators 14
1-f Convergence of Vectors 16
1-g Operator Limits 19
2 The Scattering Operator for a Single Particle 21
2-a Classical Scattering 22
2-b Quantum Scattering 25
2-c The Asymptotic Condition 28
2-d Orthogonality and Asymptotic Completeness 31
2-e The Scattering Operator 34
2- f Unitarity 36
3 Cross Sections in Terms of the S Matrix 38
3- a Conservation of Energy 39
3-b The On-Shell T Matrix and Scattering Amplitude 42
3-c The Classical Cross Section 44
3-d Definition of the Quantum Cross Section 46
3-e Calculation of the Quantum Cross Section 49
3-f The Optical Theorem 53
xi
xii Contents
4 Scattering of Two Spinless Particles 56
4-a Two-Particle Wave Functions 57
4-b The Two-Particle S Operator 60
4-c Conservation of Energy-Momentum and the T Matrix 62
4-d Cross Sections in Various Frames 64
4- e The Center-of-Mass Cross Section 66
5 Scattering of Two Particles with Spin 69
5- a The Hilbert Space for Particles with Spin 70
5-b The S Operator for Particles with Spin 72
5-c The Amplitudes and Amplitude Matrix 73
5-d Sums and Averages Over Spins 76
5- e Hie In and Out Spinors 78
6 Invariance Principles and Conservation Laws 81
6- a Translational Invariance and Conservation of Momentum 82
6-b Rotational Invariance and Conservation of Angular Momentum 83
6-c The Partial-Wave Series for Spinless Particles 85
6-d Parity 90
6-e Time Reversal 91
6-f Invariance Principles for Particles with Spin;
Momentum-Space Analysis 95
6- g Invariance Principles for Particles with Spin;
Angular-Momentum Analysis 103
7 More About Particles with Spin 109
7- a Polarization and the Density Matrix 109
7-b The In and Out Density Matrices 113
7-c Polarization Experiments in (Spin K) — (Spin 0) Scattering 114
7-d The Helicity Formalism 119
7-e Some Useful Formulas 124
Contents xiii
8 The Green’s Operator and the T Operator 128
8-a The Green's Operator 129
8-b The T Operator 134
8- c Relation to the Midler Operators 135
M Relation to the Scattering Operator 138
9 The Bom Series 143
9- a The Born Series 144
9-b The Born Approximation 147
9-c The Yukawa Potential 150
N Scattering of Electrons off Atoms 153
9- e Interpretation of the Born Series in Terms of Feynman
Diagrams 157
10 The Stationary Scattering States 164
10- a Definition and Properties of the Stationary Scattering States 105
10-b Equations for the Stationary Scattering Vectors 168
10-c The Stationary Wave Functions 170
10- d A Spatial Description of the Scattering Process 173
11 The Partial-Wave Stationary States 180
11- a The Partial-Wave S Matrix 181
11-b The Free Radial Wave Functions 182
11-c The Partial-Wave Scattering States 185
11-d The Partial-Wave Lippmann-Schwinger Equation 188
11-e Properties of the Partial-Wave Amplitude 191
11-f The Regular Solution 197
11-g The Variable Phase Method 197
11-h Iterative Solution for the Regular Wave Function 201
11-i The Jost Function 204
11-j The Partial-Wave Born Series 207
Contents
xiv
12 Analytic Properties of the Partial-Wave
Amplitude 212
12-a Analytic Functions of a Complex Variable 213
12-b Analytic Properties of the Regular Solution 215
12-c Analytic Properties of the Jost Function and S Matrix 217
12-d Bound States and Poles of the S Matrix 223
12-e Levinson’s Theorem 226
12-f Threshold Behavior and Effective Range Formulas 229
12- g Zeros of the Jost Function at Threshold 232
13 Resonances 238
13- a Resonances and Poles of the S Matrix 240
13-b Bound States and Resonances 245
13-c Time Delay 249
13- d Decay of a Resonant State 253
14 Additional Topics in Single-Channel
Scattering 259
14- a Coulomb Scattering 259
14-b Coulomb Plus Short-Range Potentials 266
14-c The Distorted-Wave Born Approximation 270
14- d Variational Methods 273
14~e The K Matrix 280
15 Dispersion Relations and Complex Angular
Momenta 285
15- a Partial-Wave Dispersion Relations 287
15-b Forward Dispersion Relations 291
15-c Nonforward Dispersion Relations 294
15-d The Mandelstam Representation 297
15-e Complex Angular Momenta 302
15-f Regge Poles 306
15-g The Watson Transform 308
Contents xv
16 The Scattering Operator in Multichannel
Scattering 315
16-a Channels 316
16-b Channel Hamiltonians and Asymptotic States 321
16-c Orthogonality and Asymptotic Completeness 326
16-d A Little More Mathematics 331
16- e The Scattering Operator 334
17 Cross Sections and Invariance Principles in
Multichannel Scattering 338
17- a The Momentum-Space Basis Vectors 339
17-b Conservation of Energy and the On-Shell T Matrix 342
17-c Cross Sections 346
17-d Rotational Invariance 351
17- e Time-Reversal Invariance 353
18 Fundamentals of Time-Independent
Multichannel Scattering 358
18- a Hie Stationary Scattering States 359
18-b Hie Lippmann-Schwinger Equations 361
18-c The T Operators '363
18-d The Born Approximation; Elastic Scattering 364
18- e The Born Approximation; Excitation 367
19 Properties of the Multichannel Stationary
Wave Functions 372
19- a Asymptotic Form of the Stationary Wave Functions;
Collisions Without Rearrangement 373
19-b Asymptotic Form of the Stationary Wave Functions;
Rearrangement Collisions 378
19-c Expansion in Terms of Target States 380
19-d The Optical Potential 383
xvi
Contents
20 Analytic Properties and Multichannel
Resonances 391
20-a Analytic Properties 392
20-b Proof of Analytic Properties 396
20-c Bound States 405
20-d Resonances 407
20- e Decay of a Multichannel Resonance 413
21 Two More Topics in Multichannel Scattering 418
21- a The Distorted-Wave Born Approximation 418
21- b Final-State Interactions 424
22 Identical Particles 434
22- a The Formalism of Identical Particles 435
22-b Scattering of Two Identical Particles 441
22-c Multichannel Scattering with Identical Particles 448
22-d Transition Probabilities and Cross Sections 450
22-e Electron-Hydrogen Scattering 454
References 463
Index |
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| id | DE-604.BV022396598 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:16:46Z |
| indexdate | 2024-07-09T20:56:42Z |
| institution | BVB |
| isbn | 0486450139 9780486450131 |
| language | English |
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| physical | XVI, 477 S. graph. Darst. |
| publishDate | 2006 |
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| publisher | Dover Publ. |
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| spelling | Taylor, John R. 1939- Verfasser (DE-588)13755785X aut Scattering theory the quantum theory on nonrelativistic collisions John R. Taylor Dover ed. Mineola, NY Dover Publ. 2006 XVI, 477 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dover books on engineering This Dover ed. is an unabridged republication of the revised ed. of the work, as publ. by Robert E. Krieger Publ. Comp., Malabar, Florida, in 1983. Nonrelativistic quantum mechanics Scattering (Physics) Streutheorie (DE-588)4183697-2 gnd rswk-swf Streutheorie (DE-588)4183697-2 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015605330&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taylor, John R. 1939- Scattering theory the quantum theory on nonrelativistic collisions Nonrelativistic quantum mechanics Scattering (Physics) Streutheorie (DE-588)4183697-2 gnd |
| subject_GND | (DE-588)4183697-2 |
| title | Scattering theory the quantum theory on nonrelativistic collisions |
| title_auth | Scattering theory the quantum theory on nonrelativistic collisions |
| title_exact_search | Scattering theory the quantum theory on nonrelativistic collisions |
| title_exact_search_txtP | Scattering theory the quantum theory on nonrelativistic collisions |
| title_full | Scattering theory the quantum theory on nonrelativistic collisions John R. Taylor |
| title_fullStr | Scattering theory the quantum theory on nonrelativistic collisions John R. Taylor |
| title_full_unstemmed | Scattering theory the quantum theory on nonrelativistic collisions John R. Taylor |
| title_short | Scattering theory |
| title_sort | scattering theory the quantum theory on nonrelativistic collisions |
| title_sub | the quantum theory on nonrelativistic collisions |
| topic | Nonrelativistic quantum mechanics Scattering (Physics) Streutheorie (DE-588)4183697-2 gnd |
| topic_facet | Nonrelativistic quantum mechanics Scattering (Physics) Streutheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015605330&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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