Verfügbarkeit: Asymptotic methods in quantum mechanics

Asymptotic methods in quantum mechanics: application to atoms, molecules and nuclei

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Bibliographische Detailangaben
Hauptverfasser:	Patil, S. H. 1940- (VerfasserIn), Tang, Kwong-Tin 1936- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin [u.a.] Springer 2000
Schriftenreihe:	Springer series in chemical physics 64
Schlagworte:	Chimie quantique Développements asymptotiques Fonctions d'onde Físico-química Asymptotic expansions Quantum chemistry Wave functions Quantenmechanik Wellenfunktion Asymptotische Methode Asymptotik Eigenfunktion Schrödinger-Gleichung
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XI, 171 S. graph. Darst.
ISBN:	3540672400

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MARC


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Datensatz im Suchindex

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adam_text	CONTENTS 1. INTRODUCTION :::::::::::::::::::::::::::::::::::::::::::::: 1 2. GENERAL PROPERTIES OF WAVE FUNCTIONS :::::::::::::::::::: 5 2.1 ASYMPTOTIC FORM OF WAVE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . 5 2.2 ASYMPTOTIC PERTURBED WAVE FUNCTION . . . . . . . . . . . . . . . . . . . . . 8 2.3 WAVE FUNCTION FOR R IJ ! 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.4 WAVE FUNCTION FOR R IJ AND R IK ! 0 . . . . . . . . . . . . . . . . . . . . . . . . 12 2.5 LOCAL SATISFACTION OF SCHR¨ ODINGER EQUATION. . . . . . . . . . . . . . . . . 13 2.6 VARIATIONAL STATIONARY PROPERTY . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.7 VARIATIONAL APPROACH TO PERTURBATIONS . . . . . . . . . . . . . . . . . . . . 15 2.8 GENERALISED VIRIAL THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.9 A SIMPLE EXAMPLE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3. TWO- AND THREE-ELECTRON ATOMS AND IONS :::::::::::::::: 21 3.1 A SIMPLE WAVE FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1.1 ENERGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1.2 MULTIPOLAR POTENTIAL PERTURBATION . . . . . . . . . . . . . . . . . . 23 3.1.3 THIRD ORDER ENERGY SHIFTS . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 WAVE FUNCTIONS SATISFYING CUSP, COALESCENCE AND ASYMPTOTIC CONDITIONS . . . . . . . . . . . . . . . . . . . 25 3.2.1 BEHAVIOUR FOR R I ! 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2.2 CORRELATION FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2.3 RESULTS FOR THE UNPERTURBED GROUND STATE . . . . . . . . . . 28 3.2.4 MULTIPOLAR POLARIZABILITIES AND HYPERPOLARIZABILITIES . . 31 3.2.5 WAVE FUNCTIONS FOR EXCITED STATES . . . . . . . . . . . . . . . . . . 33 3.3 THREE-ELECTRON WAVE FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4. POLARIZABILITIES AND DISPERSION COECIENTS ::::::::::::::: 41 4.1 POLARIZABILITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1.1 PERTURBATIVE EXPRESSION . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.1.2 HYPERPOLARIZABILITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1.3 DYNAMIC POLARIZABILITIES. . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.2 DISPERSION COECIENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2.1 RELATION TO DYNAMIC POLARIZABILITIES . . . . . . . . . . . . . . . . 48 X CONTENTS 4.2.2 THREE-BODY DISPERSION COECIENTS . . . . . . . . . . . . . . . . . 49 4.3 ALKALI ISOELECTRONIC SEQUENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.1 THE WAVE FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.2 POLARIZABILITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3.3 HYPERPOLARIZABILITIES AND DISPERSION COECIENTS . . . . . 56 4.4 ASYMPTOTIC POLARIZABILITIES AND DISPERSION COECIENTS . . . . . . 58 4.4.1 ASYMPTOTIC POLARIZABILITIES . . . . . . . . . . . . . . . . . . . . . . . . 58 4.4.2 POLARIZABILITIES OF HE AND NE SYSTEMS . . . . . . . . . . . . . . . 60 4.4.3 ASYMPTOTIC BEHAVIOUR OF THE EECTIVE ENERGY . . . . . . . 62 4.4.4 DISPERSION COECIENTS FOR H, HE AND NE . . . . . . . . . . . . 65 5. ASYMPTOTICALLY CORRECT THOMAS{FERMI MODEL DENSITY :::: 69 5.1 THOMAS{FERMI MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.1.1 STATISTICAL APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.1.2 WKB APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.2 SOLUTION FOR THE THOMAS{FERMI DENSITY . . . . . . . . . . . . . . . . . . . 71 5.3 ASYMPTOTIC DENSITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.4 MODIED DENSITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.5 APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5.1 EXPECTATION VALUES H R 2 N I . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5.2 MULTIPOLAR POLARIZABILITIES . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.5.3 DISPERSION COECIENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6. MOLECULES AND MOLECULAR IONS WITH ONE AND TWO ELECTRONS ::::::::::::::::::::::::::::: 85 6.1 WAVE FUNCTIONS FOR ONE-ELECTRON MOLECULAR IONS . . . . . . . . . . . 86 6.1.1 CUSP CONDITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.1.2 ASYMPTOTIC BEHAVIOUR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6.2 ENERGIES FOR ONE-ELECTRON MOLECULAR IONS . . . . . . . . . . . . . . . . . . 89 6.3 WAVE FUNCTION FOR H 2 AND HE ++ 2 . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.3.1 MOLECULAR ORBITAL TYPE OF WAVE FUNCTION . . . . . . . . . . . 91 6.3.2 ATOMIC ORBITAL TYPE OF WAVE FUNCTION . . . . . . . . . . . . . 92 6.3.3 GENERAL WAVE FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 6.3.4 CORRELATION FUNCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 6.4 RESULTS FOR THE GROUND STATE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.4.1 GROUND STATE ENERGIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 6.4.2 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 7. INTERACTION OF AN ELECTRON WITH IONS, ATOMS, AND MOLECULES 105 7.1 ATOMIC RYDBERG STATES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 7.1.1 PERTURBATION APPROACH FOR ANTI-SYMMETRIC WAVE FUNCTIONS . . . . . . . . . . . . . . . . . 105 7.1.2 THE PERTURBED HAMILTONIAN . . . . . . . . . . . . . . . . . . . . . . . 107 7.1.3 ASYMPTOTIC CORE DENSITY AND DENSITY MATRIX . . . . . . . . 108 7.1.4 PENETRATION ENERGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 CONTENTS XI 7.1.5 EXCHANGE ENERGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 7.1.6 SECOND ORDER TERMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 7.1.7 TOTAL ENERGY SHIFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 7.1.8 RESULTS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 7.2 ELECTRON{ATOM AND ELECTRON{MOLECULE SCATTERING AT HIGH ENERGIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.2.1 PERTURBATION SERIES FOR THE SCATTERING AMPLITUDE . . . . . 115 7.2.2 SCATTERING AMPLITUDE AT HIGH ENERGIES . . . . . . . . . . . . . . 117 7.2.3 ELECTRON{ATOM SCATTERING . . . . . . . . . . . . . . . . . . . . . . . . . 118 7.2.4 ELECTRON{MOLECULE SCATTERING . . . . . . . . . . . . . . . . . . . . . . 120 8. EXCHANGE ENERGY OF DIATOMIC SYSTEMS :::::::::::::::::::: 127 8.1 EXCHANGE ENERGY OF DIMER IONS . . . . . . . . . . . . . . . . . . . . . . . . . . 127 8.1.1 EXCHANGE ENERGY OF THE H + 2 MOLECULAR ION BY SURFACE INTEGRAL METHOD . . . . . . . . . . . . . . . . . . . . . . . . 128 8.1.2 EXCHANGE ENERGY OF MULTIELECTRON DIMER IONS . . . . . . . . 133 8.2 EXCHANGE ENERGY OF DIATOMIC MOLECULES . . . . . . . . . . . . . . . . . . . 136 8.2.1 EXCHANGE ENERGY OF THE H 2 MOLECULE . . . . . . . . . . . . . . . 136 8.2.2 EXCHANGE ENERGY OF MULTIELECTRON DIATOMIC MOLECULES 144 9. INTER-ATOMIC AND INTER-IONIC POTENTIALS :::::::::::::::::::: 147 9.1 EXCHANGE ENERGY AND EXCHANGE INTEGRAL IN THE HEITLER{LONDON THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 9.2 GENERALIZED HEITLER{LONDON THEORY . . . . . . . . . . . . . . . . . . . . . . . 150 9.2.1 UNSYMMETRIZED (POLARIZATION) PERTURBATION METHOD . . 150 9.2.2 SYMMETRY IMPOSED GENERALISED HEITLER{LONDON EQUATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 9.2.3 ASYMPTOTIC EXCHANGE ENERGY AND POLARIZATION APPROXIMATION . . . . . . . . . . . . . . . . . . . . 153 9.3 INTER-ATOMIC AND INTER-IONIC POTENTIALS . . . . . . . . . . . . . . . . . . . . 154 9.3.1 THE 3 U STATE POTENTIAL OF THE H 2 MOLECULE . . . . . . . . . 154 9.3.2 THE 2 * U STATE POTENTIALS OF ALKALI DIMER CATIONS . . . . 156 9.3.3 THE POTENTIAL OF RARE GAS DIMERS . . . . . . . . . . . . . . . . . . 157 10. PROTON AND NEUTRON DENSITIES IN NUCLEI :::::::::::::::::: 161 10.1 SEMI-PHENOMENOLOGICAL DENSITY . . . . . . . . . . . . . . . . . . . . . . . . . . 161 10.2 DETERMINATION OF THE PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . 162 10.3 RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 REFERENCES :::::::::::::::::::::::::::::::::::::::::::::::::::: 169
any_adam_object	1
author	Patil, S. H. 1940- Tang, Kwong-Tin 1936-
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id	DE-604.BV013177541
illustrated	Illustrated
indexdate	2024-07-09T18:40:21Z
institution	BVB
isbn	3540672400
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-008978669
oclc_num	43641288
open_access_boolean
owner	DE-384 DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-188
owner_facet	DE-384 DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-83 DE-11 DE-188
physical	XI, 171 S. graph. Darst.
publishDate	2000
publishDateSearch	2000
publishDateSort	2000
publisher	Springer
record_format	marc
series	Springer series in chemical physics
series2	Springer series in chemical physics
spelling	Patil, S. H. 1940- Verfasser (DE-588)121817237 aut Asymptotic methods in quantum mechanics application to atoms, molecules and nuclei S. H. Patil ; K. T. Tang Berlin [u.a.] Springer 2000 XI, 171 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in chemical physics 64 Chimie quantique ram Développements asymptotiques ram Fonctions d'onde ram Físico-química larpcal Asymptotic expansions Quantum chemistry Wave functions Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Wellenfunktion (DE-588)4189547-2 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Eigenfunktion (DE-588)4151167-0 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Schrödinger-Gleichung (DE-588)4053332-3 s Eigenfunktion (DE-588)4151167-0 s Asymptotik (DE-588)4126634-1 s DE-604 Quantenmechanik (DE-588)4047989-4 s Wellenfunktion (DE-588)4189547-2 s Asymptotische Methode (DE-588)4287476-2 s Tang, Kwong-Tin 1936- Verfasser (DE-588)121817245 aut Springer series in chemical physics 64 (DE-604)BV000000670 64 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008978669&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Patil, S. H. 1940- Tang, Kwong-Tin 1936- Asymptotic methods in quantum mechanics application to atoms, molecules and nuclei Springer series in chemical physics Chimie quantique ram Développements asymptotiques ram Fonctions d'onde ram Físico-química larpcal Asymptotic expansions Quantum chemistry Wave functions Quantenmechanik (DE-588)4047989-4 gnd Wellenfunktion (DE-588)4189547-2 gnd Asymptotische Methode (DE-588)4287476-2 gnd Asymptotik (DE-588)4126634-1 gnd Eigenfunktion (DE-588)4151167-0 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd
subject_GND	(DE-588)4047989-4 (DE-588)4189547-2 (DE-588)4287476-2 (DE-588)4126634-1 (DE-588)4151167-0 (DE-588)4053332-3
title	Asymptotic methods in quantum mechanics application to atoms, molecules and nuclei
title_auth	Asymptotic methods in quantum mechanics application to atoms, molecules and nuclei
title_exact_search	Asymptotic methods in quantum mechanics application to atoms, molecules and nuclei
title_full	Asymptotic methods in quantum mechanics application to atoms, molecules and nuclei S. H. Patil ; K. T. Tang
title_fullStr	Asymptotic methods in quantum mechanics application to atoms, molecules and nuclei S. H. Patil ; K. T. Tang
title_full_unstemmed	Asymptotic methods in quantum mechanics application to atoms, molecules and nuclei S. H. Patil ; K. T. Tang
title_short	Asymptotic methods in quantum mechanics
title_sort	asymptotic methods in quantum mechanics application to atoms molecules and nuclei
title_sub	application to atoms, molecules and nuclei
topic	Chimie quantique ram Développements asymptotiques ram Fonctions d'onde ram Físico-química larpcal Asymptotic expansions Quantum chemistry Wave functions Quantenmechanik (DE-588)4047989-4 gnd Wellenfunktion (DE-588)4189547-2 gnd Asymptotische Methode (DE-588)4287476-2 gnd Asymptotik (DE-588)4126634-1 gnd Eigenfunktion (DE-588)4151167-0 gnd Schrödinger-Gleichung (DE-588)4053332-3 gnd
topic_facet	Chimie quantique Développements asymptotiques Fonctions d'onde Físico-química Asymptotic expansions Quantum chemistry Wave functions Quantenmechanik Wellenfunktion Asymptotische Methode Asymptotik Eigenfunktion Schrödinger-Gleichung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008978669&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000670
work_keys_str_mv	AT patilsh asymptoticmethodsinquantummechanicsapplicationtoatomsmoleculesandnuclei AT tangkwongtin asymptoticmethodsinquantummechanicsapplicationtoatomsmoleculesandnuclei

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