Scattering theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Dordrecht ; London
Springer
[2016]
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | http://www.springer.com/ Inhaltstext Inhaltsverzeichnis |
| Physical Description: | xiii, 287 Seiten Diagramme |
| ISBN: | 3662485249 9783662485248 |
Staff View
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| 245 | 1 | 0 | |a Scattering theory |c Harald Friedrich |
| 250 | |a Second edition | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Dordrecht ; London |b Springer |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xiii, 287 Seiten |b Diagramme | ||
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| 650 | 0 | 7 | |a Streutheorie |0 (DE-588)4183697-2 |2 gnd |9 rswk-swf |
| 653 | |a Research | ||
| 653 | |a PHM | ||
| 653 | |a Inelastic Scattering Physics | ||
| 653 | |a Elastic Scattering Physics | ||
| 653 | |a Scattering Cross Section | ||
| 653 | |a Lippmann Schwinger Equation | ||
| 653 | |a Projectile Target Interaction | ||
| 653 | |a Feshbach Resonance | ||
| 653 | |a Scattering Ultracold Atom | ||
| 653 | |a Scattering Theory Physics | ||
| 653 | |a Coulomb Potential Scattering | ||
| 653 | |a WKB Approximation | ||
| 653 | |a Scattering Ultracold Molecule | ||
| 653 | |a Born Approximation | ||
| 653 | |a Multichannel Quantum Defect | ||
| 653 | |a Quantum Description Scattering | ||
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Record in the Search Index
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CONTENTS
1 CLASSICAL SCATTERING THEORY 1
1.1 RELATIVE MOTION OF PROJECTILE AND TARGET 1
1.2 DEFLECTION FUNCTION 2
1.2.1 KEPLER-COULOMB POTENTIAL 5
1.2.2 INVERSE-POWER POTENTIALS 6
1.2.3 LENNARD-JONES POTENTIAL 9
1.3 SCATTERING ANGLE AND SCATTERING CROSS SECTIONS 11
1.3.1 KEPLER-COULOMB POTENTIAL 13
1.3.2 INVERSE-POWER POTENTIALS 14
1.3.3 LENNARD-JONES POTENTIAL 16
1.4 CLASSICAL SCATTERING IN TWO SPATIAL DIMENSIONS 17
REFERENCES 21
2 ELASTIC SCATTERING BY A CONSERVATIVE POTENTIAL 23
2.1 SCATTERING AMPLITUDE AND SCATTERING CROSS SECTION 23
2.2 LIPPMANN-SCHWINGER EQUATION AND BORN APPROXIMATION . 26
2.3 RADIALLY SYMMETRIC POTENTIALS 28
2.3.1 ANGULAR MOMENTUM 28
2.3.2 PARTIAL-WAVES EXPANSION 29
2.3.3 SCATTERING PHASE SHIFTS 30
2.3.4 NORMALIZATION OF RADIAL WAVE FUNCTIONS 33
2.3.5 RADIAL LIPPMANN-SCHWINGER EQUATION 34
2.3.6 S-MATRIX 36
2.3.7 DETERMINATION OF THE SCATTERING PHASE SHIFTS 37
2.3.8 NEAR-THRESHOLD BEHAVIOUR OF THE SCATTERING PHASE SHIFTS 38
2.3.9 LEVINSON'S THEOREM 45
2.3.10 POTENTIAL RESONANCES (SHAPE RESONANCES) 49
2.3.11 SCATTERING CROSS SECTIONS 55
2.4 THE WKB APPROXIMATION 58
2.4.1 DEFINITION AND ACCURACY OF WKB WAVE FUNCTIONS . 58
2.4.2 CONNECTION ACROSS A CLASSICAL TURNING POINT 60
XI
HTTP://D-NB.INFO/1075881129
XII CONTENTS
2.4.3 WKB PHASE SHIFTS 67
2.5 COULOMBIC POTENTIALS 70
2.5.1 PURE COULOMB POTENTIAL 71
2.5.2 MODIFIED COULOMB POTENTIAL; GENERAL CONSIDERATIONS . . 75
2.5.3 MODIFIED REPULSIVE COULOMB POTENTIAL 78
2.5.4 MODIFIED ATTRACTIVE COULOMB POTENTIAL, QUANTUM-DEFECT
THEORY 81
2.6 POTENTIALS FALLING OFF AS 1/R", A 2 90
2.6.1 NEAR-THRESHOLD BEHAVIOUR OF SCATTERING PHASE SHIFTS . . 90
2.6.2 THE SPECIAL CASE 21 + 3 = A 93
2.6.3 MODIFIED EFFECTIVE-RANGE EXPANSIONS 95
2.6.4 PERIPHERAL SCATTERING 98
2.6.5 THE LENNARD-JONES POTENTIAL 99
2.7 POTENTIALS WITH INVERSE-SQUARE TAILS 101
2.7.1 PURE INVERSE-SQUARE POTENTIAL 101
2.7.2 MODIFIED INVERSE-SQUARE POTENTIAL 106
2.7.3 EXAMPLE: INVERSE-SQUARE POTENTIAL WITH HARD SPHERE . . . 110
2.8 NONVANISHING ANGULAR MOMENTUM OF PROJECTILE AND/OR TARGET . . 113
2.8.1 GENERAL FORMALISM FOR TREATING SPINS 113
2.8.2 SPIN-J PROJECTILE WITH SPIN-ZERO TARGET 119
2.8.3 APPLICATION TO MIXED SPIN STATES 124
2.9 WHEN PROJECTILE AND TARGET ARE INDISTINGUISHABLE 126
2.9.1 SPINLESS BOSONS 126
2.9.2 SPIN-J FERMIONS 130
REFERENCES 133
3 INTERNAL EXCITATION, INELASTIC SCATTERING 137
3.1 COUPLED-CHANNEL EQUATIONS AND SCATTERING CROSS SECTIONS . . 137
3.2 COUPLED-CHANNEL LIPPMANN-SCHWINGER EQUATION AND BORN
APPROXIMATION 140
3.3 RADIAL COUPLED-CHANNEL EQUATIONS 142
3.4 ABSORPTION 146
3.5 FESHBACH RESONANCES 147
3.5.1 SINGLE ISOLATED FESHBACH RESONANCE 148
3.5.2 INTERFERING RESONANCES 156
3.5.3 RESONANCES IN THE PRESENCE OF SEVERAL OPEN CHANNELS . . 161
3.6 COULOMBIC POTENTIALS, GENERAL THEORY 163
3.6.1 SCATTERING CROSS SECTIONS 163
3.6.2 PARTIAL-WAVES EXPANSION 164
3.7 ATTRACTIVE COULOMB POTENTIALS, MULTICHANNEL QUANTUM-DEFECT
THEORY 166
3.7.1 PERTURBED RYDBERG SERIES 167
3.7.2 TWO COUPLED COULOMBIC CHANNELS 169
3.7.3 MORE THAN TWO COUPLED COULOMBIC CHANNELS 177
REFERENCES 183
CONTENTS XIII
4 SPECIAL TOPICS 185
4.1 DEEP POTENTIALS FALLING OFF FASTER THAN 1/R
2
ASYMPTOTICALLY . . . 185
4.1.1 NEAR-THRESHOLD QUANTIZATION 185
4.1.2 QUANTUM REFLECTION 209
4.1.3 ELASTIC SCATTERING 220
4.1.4 NONVANISHING ANGULAR MOMENTUM 229
4.1.5 SUMMARY 232
4.1.6 RELATION TO OTHER APPROACHES 234
4.2 NEAR-THRESHOLD FESHBACH RESONANCES 236
4.2.1 MOTIVATION 236
4.2.2 THRESHOLD-INSENSITIVE PARAMETRIZATION OF A FESHBACH
RESONANCE 238
4.2.3 INFLUENCE ON THE SCATTERING LENGTH 241
4.2.4 INFLUENCE ON THE BOUND-STATE SPECTRUM 243
4.2.5 RELATION TO THE EMPIRICAL FORMULA (4.157) 246
4.3 QUANTUM DESCRIPTION OF SCATTERING IN TWO SPATIAL DIMENSIONS 248
4.3.1 SCATTERING AMPLITUDE AND SCATTERING CROSS SECTION . . . . 249
4.3.2 LIPPMANN-SCHWINGER EQUATION AND BORN APPROXIMATION 250
4.3.3 PARTIAL-WAVES EXPANSION AND SCATTERING PHASE SHIFTS . 251
4.3.4 NEAR-THRESHOLD BEHAVIOUR OF THE SCATTERING PHASE SHIFTS 254
4.3.5 THE CASE M * 0, S-WAVES IN TWO DIMENSIONS 255
4.3.6 RUTHERFORD SCATTERING IN TWO DIMENSIONS 259
REFERENCES 261
APPENDIX A SCALING 267
A.L CLASSICAL MECHANICS 267
A.2 QUANTUM MECHANICS 269
REFERENCES 271
APPENDIX B SPECIAL FUNCTIONS 273
B.L LEGENDRE POLYNOMIALS, SPHERICAL HARMONICS 273
B.2 ERROR FUNCTION 274
B.3 GAMMA FUNCTION 274
B.4 BESSEL FUNCTIONS 275
B.5 CONFLUENT HYPERGEOMETRIC FUNCTIONS, COULOMB FUNCTIONS,
WHITTAKER'S FUNCTION 279
REFERENCES 281
INDEX 283 |
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| author | Friedrich, Harald 1947-2017 |
| author_GND | (DE-588)11819738X |
| author_facet | Friedrich, Harald 1947-2017 |
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| author_variant | h f hf |
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| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | Second edition |
| format | Book |
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| spelling | Friedrich, Harald 1947-2017 Verfasser (DE-588)11819738X aut Scattering theory Harald Friedrich Second edition Berlin ; Heidelberg ; New York ; Dordrecht ; London Springer [2016] © 2016 xiii, 287 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Streutheorie (DE-588)4183697-2 gnd rswk-swf Research PHM Inelastic Scattering Physics Elastic Scattering Physics Scattering Cross Section Lippmann Schwinger Equation Projectile Target Interaction Feshbach Resonance Scattering Ultracold Atom Scattering Theory Physics Coulomb Potential Scattering WKB Approximation Scattering Ultracold Molecule Born Approximation Multichannel Quantum Defect Quantum Description Scattering Streutheorie (DE-588)4183697-2 s DE-604 Springer-Verlag GmbH (DE-588)1065168780 pbl Erscheint auch als Online-Ausgabe 978-3-662-48526-2 http://www.springer.com/ Verlag X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=71e2427a017646e0af7d266a76783200&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=028605778&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Friedrich, Harald 1947-2017 Scattering theory Streutheorie (DE-588)4183697-2 gnd |
| subject_GND | (DE-588)4183697-2 |
| title | Scattering theory |
| title_auth | Scattering theory |
| title_exact_search | Scattering theory |
| title_full | Scattering theory Harald Friedrich |
| title_fullStr | Scattering theory Harald Friedrich |
| title_full_unstemmed | Scattering theory Harald Friedrich |
| title_short | Scattering theory |
| title_sort | scattering theory |
| topic | Streutheorie (DE-588)4183697-2 gnd |
| topic_facet | Streutheorie |
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