Scattering theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Lecture notes in physics
872 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XI, 287 S. graph. Darst. |
| ISBN: | 9783642382819 |
Staff View
MARC
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| 100 | 1 | |a Friedrich, Harald |d 1947-2017 |e Verfasser |0 (DE-588)11819738X |4 aut | |
| 245 | 1 | 0 | |a Scattering theory |c Harald Friedrich |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XI, 287 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804150669924368384 |
|---|---|
| adam_text | Contents
Classical Scattering Theory
....................... 1
1.1
Relatíve
Motion of Projectile and Target
..............
I
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
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
SMatrix
........................... 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
Potentiai 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
ix
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 /ra,a>2
................ 90
2.6.1
Near-Threshold Behaviour of Scattering Phase Shifts
... 90
2.6.2
The Special Case
2! + 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-1 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-4
Fermions
....................... 130
References
................................. 133
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
Xl
Special
Topics...............................
185
4.1 Deep Potentials
Falling off Faster than 1/r2 Asymptotically
.... 185
4.
4.
4.
4.
4.
4.
.1
о
.3
.4
.5
.6
Near-Threshold Quantization
................ 185
Quantum Reflection
..................... 209
Elastic Scattering
...................... 220
Nonvanishing Angular Momentum
............. 229
Summan,
........................... 232
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
(4.156)......... 246
4.3
Quantum Description of Scattering in Two Spatial Dimensions
. . 248
4.3.1
Scattering Amplitude and Scattering Cross Section
..... 249
Lippmann-Schw
inger
Equation and Born Approximation
. 250
Partial-Waves Expansion and Scattering Phase Shifts
.... 251
Near-Threshold Behaviour of the Scattering Phase Shifts
. 254
The Case
/// = 0,
л
-Waves in Two Dimensions
....... 255
4.3.2
4.3.3
4.3.4
4.3.5
4.3.6
References
Rutherford Scattering in Two Dimensions
.........259
.................................261
Appendix A Scaling
............................. 267
A.I Classical Mechanics
......................... 267
A.
2
Quantum Mechanics
......................... 269
References
................................. 271
Appendix
В
Special Functions
....................... 273
B.
1
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
Harald
Friedrich
Scattering Theory
Iliis book presents a concise and modern coverage of scattering theory. It is motivated
by the fact that experimental advances have shifted and broadened the scope of
applications where concepts from scattering theory are used, e.g. to the field of
ultracoki
atoms and molecules, which has been experiencing enormous growth in recent years,
largely triggered by the successful realization of
Bose-Einstein
condensates of dilute
atomic gases in
1995.
In the present treatment, special attention is given to the role played by the long-
range behaviour of the projectile-target interaction, and a theory is developed, which
is well suited to describe near-threshold bound and continuum states in realistic binary
s stems Mich as diatomic molecules or molecular ions.
lhe
level of abstraction is kept as low as at all possible, and deeper questions related
to mathematical foundations of scattering theory are passed by. The book should
be understandable for anyone with a basic knowledge ot nonrelativistic quantum
mechanics. It is intended for advanced students and researchers and it is hoped that
it will be useful for theorists and experimentalists alike.
|
| any_adam_object | 1 |
| author | Friedrich, Harald 1947-2017 |
| author_GND | (DE-588)11819738X |
| author_facet | Friedrich, Harald 1947-2017 |
| author_role | aut |
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| author_variant | h f hf |
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| bvnumber | BV041229145 |
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| classification_tum | PHY 027f |
| ctrlnum | (OCoLC)855042208 (DE-599)BSZ391928309 |
| 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 |
| format | Book |
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| id | DE-604.BV041229145 |
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| indexdate | 2024-07-10T00:42:36Z |
| institution | BVB |
| isbn | 9783642382819 |
| language | English |
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| physical | XI, 287 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Friedrich, Harald 1947-2017 Verfasser (DE-588)11819738X aut Scattering theory Harald Friedrich Berlin [u.a.] Springer 2013 XI, 287 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 872 Streutheorie (DE-588)4183697-2 gnd rswk-swf Streutheorie (DE-588)4183697-2 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-38282-6 Lecture notes in physics 872 (DE-604)BV000003166 872 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026203545&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026203545&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Friedrich, Harald 1947-2017 Scattering theory Lecture notes in physics 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 |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026203545&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026203545&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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