Quantization and scattering in the presence of singular attractive potential tails:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Hochschulschrift/Dissertation Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
2013
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| Schlagwörter: | |
| Links: | http://mediatum.ub.tum.de/node?id=1121294 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130117-1121294-0-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025894552&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 113 S. graph. Darst. |
Internformat
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| 100 | 1 | |a Müller, Tim-Oliver |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantization and scattering in the presence of singular attractive potential tails |c Tim-Oliver Müller |
| 264 | 1 | |c 2013 | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0001 DM 30839 |
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CONTENTS
LIST O F FIGURES 5
LIST O F TABLES 7
1 INTRODUCTION 9
2 THEORETICAL FRAMEWORK 1 3
2.1 SCATTERING AND QUANTIZATION 13
2.1.1 SCHRODINGER EQUATION AND PARTIAL WAVE ANALYSIS 13
2.1.2 CROSS SECTIONS AND THE SCATTERING WAVE FUNCTION 15
2.2 THE W K B APPROXIMATION 18
2.2.1 T H E SEMICLASSICAL WAVE FUNCTION 18
2.2.2 CONDITIONS OF VALIDITY 19
2.2.3 PRESENCE OF CLASSICAL TURNING POINTS 20
3 TAIL-BASED FORMULATION 2 3
3.1 THE SHORT-RANGE REGION 23
3.2 FORMULATION FOR BOUND STATES 27
3.2.1 QUANTIZATION FUNCTION 27
3.2.2 LIMITING EXPANSIONS 29
3.3 FORMULATION FOR SCATTERING STATES 31
3.3.1 PARAMETRIZATION OF THE SCATTERING PHASE SHIFT 31
3.3.2 CONNECTION TO THE PROPERTIES OF QUANTUM REFLECTION 32
3.3.3 LIMITING EXPANSIONS 35
3.4 SUMMARY OF RESULTS 41
4 APPLICATION T O INVERSE-POWER TAILS 4 3
4.1 GENERALITIES FOR INVERSE-POWER TAILS 43
4.2 QUANTIZATION FOR INVERSE-POWER TAILS 47
4.2.1 T H E GENERAL CASE - C A / R A WITH A 2 47
4.2.2 DIPOLE-DIPOLE INTERACTIONS ( A = 3) 49
4.3 SCATTERING FOR INVERSE-POWER TAILS 55
4.3.1 T H E GENERAL CASE - C A / R A W I T H A 2 55
4.3.2 INDUCED DIPOLAR INTERACTIONS ( A = 6) 62
4.3.3 QUADRUPOLE-QUADRUPOLE INTERACTIONS ( A = 5) 67
4.3.4 POLARIZATION INTERACTIONS ( A = 4) 72
3
HTTP://D-NB.INFO/1035190737
IMAGE 2
4 CONTENTS
4.3.5 DIPOLE-DIPOLE INTERACTIONS ( A = 3) 76
4.4 SUMMARY OF RESULTS 80
5 APPLICATION T O SPECIFIC S Y S T E M S 8 3
5.1 VIBRATIONAL BOUND STATES IN LONG-RANGE MOLECULES 83
5.1.1 DETERMINATION OF T H E POTENTIAL TAIL S DISPERSION COEFFICIENT 83
5.1.2 EXTRAPOLATION A N D NUMBER OF BOUND STATES 84
5.2 APPLICATION T O MODEL POTENTIALS 87
5.2.1 (12(6) LENNARD-JONES POTENTIAL 88
5.2.2 (6|3) LENNARD-JONES POTENTIAL 90
5.2.3 MODEL POTENTIAL WITH A MIXED TAIL 93
5.3 SUMMARY OF RESULTS 96
6 CONCLUSIONS A N D O U T L O O K 9 7
A P P E N D I X 101
A INTERATOMIC POTENTIALS 1 0 1
B T H E TRANSMISSION A M P L I T U D E 1 0 5
C VERIFICATION O F A S Y M P T O T I C E X P A N S I O N S 1 0 7
BIBLIOGRAPHY 1 0 9
|
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| indexdate | 2024-12-20T16:27:05Z |
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| language | English |
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| physical | 113 S. graph. Darst. |
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| spellingShingle | Müller, Tim-Oliver Quantization and scattering in the presence of singular attractive potential tails |
| subject_GND | (DE-588)4113937-9 |
| title | Quantization and scattering in the presence of singular attractive potential tails |
| title_auth | Quantization and scattering in the presence of singular attractive potential tails |
| title_exact_search | Quantization and scattering in the presence of singular attractive potential tails |
| title_full | Quantization and scattering in the presence of singular attractive potential tails Tim-Oliver Müller |
| title_fullStr | Quantization and scattering in the presence of singular attractive potential tails Tim-Oliver Müller |
| title_full_unstemmed | Quantization and scattering in the presence of singular attractive potential tails Tim-Oliver Müller |
| title_short | Quantization and scattering in the presence of singular attractive potential tails |
| title_sort | quantization and scattering in the presence of singular attractive potential tails |
| topic_facet | Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1121294 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130117-1121294-0-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025894552&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mullertimoliver quantizationandscatteringinthepresenceofsingularattractivepotentialtails |
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