Holdings: Stochastic variational approach to quantum-mechanical few-body problems

Stochastic variational approach to quantum-mechanical few-body problems:

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Bibliographic Details
Main Authors:	Suzuki, Yasuyuki 1945- (Author), Varga, Kálmán (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 1998
Series:	Lecture notes in physics New series : M, Monographs ; 54
Subjects:	Quantentheorie Few-body problem Quantum theory Random variables Schrödinger-Gleichung Wenigteilchensystem Stochastische Optimierung Variationsrechnung Stochastik Quantenmechanisches System Vielkörperproblem Eigenwert Variationsproblem Quantenmechanik
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. [299] - 305
Physical Description:	XIV, 310 S. graph. Darst.
ISBN:	3540651527

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adam_text	YASUYUKI SUZUKI KAIMAN VARGA STOCHASTIC VARIATIONAL APPROACH TO QUANTUM-MECHANICAL FEW-BODY PROBLEMS TABLE OF CONTENTS 1. INTRODUCTION 1 2. QUANTUM-MECHANICAL FEW-BODY PROBLEMS 7 2.1 HAMILTONIAN 7 2.2 RELATIVE COORDINATES 9 2.3 SYMMETRIZATION 15 2.4 PERMUTATION OF THE JACOBI COORDINATES 16 COMPLEMENTS 18 C2.1 AN JV-PARTICLE HAMILTONIAN IN THE HEAVY-PARTICLE CENTER COORDINATE SET 18 C2.2 CANONICAL JACOBI COORDINATES 19 3. INTRODUCTION TO VARIATIONAL METHODS 21 3.1 VARIATIONAL PRINCIPLES 21 3.2 THE VARIANCE OF LOCAL ENERGY 30 3.3 THE VIRIAL THEOREM 33 4. STOCHASTIC VARIATIONAL METHOD 39 4.1 BASIS OPTIMIZATION 39 4.2 A PRACTICAL EXAMPLE 43 4.2.1 GEOMETRIE PROGRESSION 44 4.2.2 RANDOM TEMPERING 47 4.2.3 RANDOM BASIS 47 4.2.4 SORTING 50 4.2.5 TRIAL AND ERROR SEARCH 50 4.2.6 REFINING 53 4.2.7 COMPARISON OF DIFFERENT OPTIMIZING STRATEGIES .. 54 4.3 OPTIMIZATION FOR EXCITED STATES 56 COMPLEMENTS 61 XII TABLE OF CONTENTS C4.1 MINIMIZATION OF ENERGY VERSUS VARIANCE 61 5. OTHER METHODS TO SOLVE FEW-BODY PROBLEMS 65 5.1 QUANTUM MONTE CARLO METHOD: THE IMAGINARY-TIME EVOLUTION OF A SYSTEM 65 5.2 HYPERSPHERICAL HARMONICS EXPANSION METHOD 67 5.3 FADDEEV METHOD 70 5.4 THE GENERATOR COORDINATE METHOD 72 6. VARIATIONAL TRIAL FUNCTIONS 75 6.1 CORRELATED GAUSSIANS AND CORRELATED GAUSSIAN-TYPE GEMINALS 75 6.2 ORBITAL FUNCTIONS WITH ARBITRARY ANGULAR MOMENTUM . . 82 6.3 GENERATING FUNCTION 87 6.4 THE SPIN FUNCTION 94 COMPLEMENTS 96 C6.1 NODELESS HARMONIC-OSCILLATOR FUNCTIONS AS A BASIS 96 C6.2 SOLID SPHERICAL HARMONICS 105 C6.3 ANGULAR MOMENTUM RECOUPLING 106 C6.4 SEPARATION OF THE CENTER-OF-MASS MOTION FROM CORRELATED GAUSSIANS 112 C6.5 THREE ELECTRONS WITH S = 1/2 115 C6.6 FOUR ELECTRONS IN AN ARBITRARY SPIN ARRANGEMENT 115 C6.7 SIX ELECTRONS WITH 5 = 0 116 EXERCISES 118 7. MATRIX ELEMENTS FOR SPHERICAL GAUSSIANS 123 7.1 MATRIX ELEMENTS OF THE GENERATING FUNCTION 123 7.2 CORRELATED GAUSSIANS 125 7.3 CORRELATED GAUSSIANS IN TWO-DIMENSIONAL SYSTEMS 129 7.4 CORRELATED GAUSSIAN-TYPE GEMINALS 131 7.5 NONLOCAL POTENTIALS 134 7.6 SEMIRELATIVISTIC KINETIC ENERGY 137 COMPLEMENTS 143 C7.1 SHERMAN-MORRISON FORMULA 143 EXERCISES 145 TABLE OF CONTENTS XIII 8. SMALL ATOMS AND MOLECULES 149 8.1 COULOMBIC SYSTEMS 149 8.2 COULOMBIC THREE-BODY SYSTEMS 150 8.3 FOUR OR MORE PARTICLES 154 8.4 SMALL MOLECULES 165 CORNPLEMENTS 167 C8.1 THE CUSP CONDITION FOR THE COULOMB POTENTIAL 167 C8.2 THE CHEMICAL BOND: THE H^ ION 169 C8.3 STABILITY OF HYDROGEN-LIKE MOLECULES 171 C8.4 APPLICATION OF GLOBAL VECTORS TO MUONIC MOLECULES .... 174 9. BARYON SPECTROSCOPY 177 9.1 THE TRIAL FUNCTION IN THE CONSTITUENT QUARK MODEL 178 9.2 ONE-GLUON EXCHANGE MODEL 178 9.3 MESON-EXCHANGE MODEL 181 10. FEW-BODY PROBLEMS IN SOLID STATE PHYSICS 187 10.1 EXCITONIC COMPLEXES 188 10.2 QUANTUM DOTS 191 10.3 QUANTUM DOTS IN MAGNETIC FIELD 196 10.4 QUANTUM DOTS IN THE GENERATOR COORDINATE METHOD.... 202 CORNPLEMENTS 204 CLO.L TWO-DIMENSIONAL ELECTRON MOTION IN A MAGNETIC FIELD . 204 11. NUCLEAR FEW-BODY SYSTEMS 213 11.1 INTRODUCTORY REMARK ON NUCLEON-NUCLEON POTENTIALS . . . 213 11.2 FEW-NUCLEON SYSTEMS WITH CENTRAL FORCES 216 11.3 REALISTIC POTENTIALS 223 CORNPLEMENTS 230 CLL.L CORRELATIONS IN FEW-NUCLEON SYSTEMS 230 CLL.2 CONVERGENCE OF PARTIAL-WAVE EXPANSIONS 233 CIL 3 QUARK PAULI EFFECT IN S-SHELL A HYPERNUCLEI 239 CLL.4 THE 12 C NUCLEUS AS A SYSTEM OF THREE ALPHA-PARTICLES . 242 APPENDIX 247 MATRIX ELEMENTS FOR GENERAL GAUSSIANS 247 A.L CORRELATED GAUSSIANS 247 A.L.L OVERLAP OF THE BASIS FUNETIONS 247 A.L.2 KINETIC ENERGY 249 XIV TABLE OF CONTENTS A.1.3 TWO-BODY INTERACTIONS 250 A.1.4 DENSITY RNULTIPOLE OPERATORS 256 A.2 CORRELATED GAUSSIANS WITH DIFFERENT COORDINATE SETS . . . 257 A.3 CORRELATED GAUSSIAN-TYPE GEMINALS 262 A.4 SPIN MATRIX ELEMENTS 263 A.5 THREE-BODY PROBLEM WITH CENTRAL, TENSOR AND SPIN-ORBIT FORCES 265 COMPLEMENTS 280 CA.L MATRIX ELEMENTS OF CENTRAL POTENTIALS 280 CA.2 MATRIX ELEMENTS OF DENSITY MULTIPOLES 283 CA.3 OVERLAP MATRIX ELEMENTS OF THE CORRELATED GAUSSIANS FOR A THREE-PARTICLE SYSTEM 285 EXERCISES 288 REFERENCES 299 INDEX 307
adam_txt	YASUYUKI SUZUKI KAIMAN VARGA STOCHASTIC VARIATIONAL APPROACH TO QUANTUM-MECHANICAL FEW-BODY PROBLEMS TABLE OF CONTENTS 1. INTRODUCTION 1 2. QUANTUM-MECHANICAL FEW-BODY PROBLEMS 7 2.1 HAMILTONIAN 7 2.2 RELATIVE COORDINATES 9 2.3 SYMMETRIZATION 15 2.4 PERMUTATION OF THE JACOBI COORDINATES 16 COMPLEMENTS 18 C2.1 AN JV-PARTICLE HAMILTONIAN IN THE HEAVY-PARTICLE CENTER COORDINATE SET 18 C2.2 CANONICAL JACOBI COORDINATES 19 3. INTRODUCTION TO VARIATIONAL METHODS 21 3.1 VARIATIONAL PRINCIPLES 21 3.2 THE VARIANCE OF LOCAL ENERGY 30 3.3 THE VIRIAL THEOREM 33 4. STOCHASTIC VARIATIONAL METHOD 39 4.1 BASIS OPTIMIZATION 39 4.2 A PRACTICAL EXAMPLE 43 4.2.1 GEOMETRIE PROGRESSION 44 4.2.2 RANDOM TEMPERING 47 4.2.3 RANDOM BASIS 47 4.2.4 SORTING 50 4.2.5 TRIAL AND ERROR SEARCH 50 4.2.6 REFINING 53 4.2.7 COMPARISON OF DIFFERENT OPTIMIZING STRATEGIES . 54 4.3 OPTIMIZATION FOR EXCITED STATES 56 COMPLEMENTS 61 XII TABLE OF CONTENTS C4.1 MINIMIZATION OF ENERGY VERSUS VARIANCE 61 5. OTHER METHODS TO SOLVE FEW-BODY PROBLEMS 65 5.1 QUANTUM MONTE CARLO METHOD: THE IMAGINARY-TIME EVOLUTION OF A SYSTEM 65 5.2 HYPERSPHERICAL HARMONICS EXPANSION METHOD 67 5.3 FADDEEV METHOD 70 5.4 THE GENERATOR COORDINATE METHOD 72 6. VARIATIONAL TRIAL FUNCTIONS 75 6.1 CORRELATED GAUSSIANS AND CORRELATED GAUSSIAN-TYPE GEMINALS 75 6.2 ORBITAL FUNCTIONS WITH ARBITRARY ANGULAR MOMENTUM . . 82 6.3 GENERATING FUNCTION 87 6.4 THE SPIN FUNCTION 94 COMPLEMENTS 96 C6.1 NODELESS HARMONIC-OSCILLATOR FUNCTIONS AS A BASIS 96 C6.2 SOLID SPHERICAL HARMONICS 105 C6.3 ANGULAR MOMENTUM RECOUPLING 106 C6.4 SEPARATION OF THE CENTER-OF-MASS MOTION FROM CORRELATED GAUSSIANS 112 C6.5 THREE ELECTRONS WITH S = 1/2 115 C6.6 FOUR ELECTRONS IN AN ARBITRARY SPIN ARRANGEMENT 115 C6.7 SIX ELECTRONS WITH 5 = 0 116 EXERCISES 118 7. MATRIX ELEMENTS FOR SPHERICAL GAUSSIANS 123 7.1 MATRIX ELEMENTS OF THE GENERATING FUNCTION 123 7.2 CORRELATED GAUSSIANS 125 7.3 CORRELATED GAUSSIANS IN TWO-DIMENSIONAL SYSTEMS 129 7.4 CORRELATED GAUSSIAN-TYPE GEMINALS 131 7.5 NONLOCAL POTENTIALS 134 7.6 SEMIRELATIVISTIC KINETIC ENERGY 137 COMPLEMENTS 143 C7.1 SHERMAN-MORRISON FORMULA 143 EXERCISES 145 TABLE OF CONTENTS XIII 8. SMALL ATOMS AND MOLECULES 149 8.1 COULOMBIC SYSTEMS 149 8.2 COULOMBIC THREE-BODY SYSTEMS 150 8.3 FOUR OR MORE PARTICLES 154 8.4 SMALL MOLECULES 165 CORNPLEMENTS 167 C8.1 THE CUSP CONDITION FOR THE COULOMB POTENTIAL 167 C8.2 THE CHEMICAL BOND: THE H^ ION 169 C8.3 STABILITY OF HYDROGEN-LIKE MOLECULES 171 C8.4 APPLICATION OF GLOBAL VECTORS TO MUONIC MOLECULES . 174 9. BARYON SPECTROSCOPY 177 9.1 THE TRIAL FUNCTION IN THE CONSTITUENT QUARK MODEL 178 9.2 ONE-GLUON EXCHANGE MODEL 178 9.3 MESON-EXCHANGE MODEL 181 10. FEW-BODY PROBLEMS IN SOLID STATE PHYSICS 187 10.1 EXCITONIC COMPLEXES 188 10.2 QUANTUM DOTS 191 10.3 QUANTUM DOTS IN MAGNETIC FIELD 196 10.4 QUANTUM DOTS IN THE GENERATOR COORDINATE METHOD. 202 CORNPLEMENTS 204 CLO.L TWO-DIMENSIONAL ELECTRON MOTION IN A MAGNETIC FIELD . 204 11. NUCLEAR FEW-BODY SYSTEMS 213 11.1 INTRODUCTORY REMARK ON NUCLEON-NUCLEON POTENTIALS . . . 213 11.2 FEW-NUCLEON SYSTEMS WITH CENTRAL FORCES 216 11.3 REALISTIC POTENTIALS 223 CORNPLEMENTS 230 CLL.L CORRELATIONS IN FEW-NUCLEON SYSTEMS 230 CLL.2 CONVERGENCE OF PARTIAL-WAVE EXPANSIONS 233 CIL 3 QUARK PAULI EFFECT IN S-SHELL A HYPERNUCLEI 239 CLL.4 THE 12 C NUCLEUS AS A SYSTEM OF THREE ALPHA-PARTICLES . 242 APPENDIX 247 MATRIX ELEMENTS FOR GENERAL GAUSSIANS 247 A.L CORRELATED GAUSSIANS 247 A.L.L OVERLAP OF THE BASIS FUNETIONS 247 A.L.2 KINETIC ENERGY 249 XIV TABLE OF CONTENTS A.1.3 TWO-BODY INTERACTIONS 250 A.1.4 DENSITY RNULTIPOLE OPERATORS 256 A.2 CORRELATED GAUSSIANS WITH DIFFERENT COORDINATE SETS . . . 257 A.3 CORRELATED GAUSSIAN-TYPE GEMINALS 262 A.4 SPIN MATRIX ELEMENTS 263 A.5 THREE-BODY PROBLEM WITH CENTRAL, TENSOR AND SPIN-ORBIT FORCES 265 COMPLEMENTS 280 CA.L MATRIX ELEMENTS OF CENTRAL POTENTIALS 280 CA.2 MATRIX ELEMENTS OF DENSITY MULTIPOLES 283 CA.3 OVERLAP MATRIX ELEMENTS OF THE CORRELATED GAUSSIANS FOR A THREE-PARTICLE SYSTEM 285 EXERCISES 288 REFERENCES 299 INDEX 307
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id	DE-604.BV022054961
illustrated	Illustrated
index_date	2024-07-02T16:13:24Z
indexdate	2024-07-09T20:49:55Z
institution	BVB
isbn	3540651527
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-015269689
oclc_num	40104946
open_access_boolean
owner	DE-706
owner_facet	DE-706
physical	XIV, 310 S. graph. Darst.
publishDate	1998
publishDateSearch	1998
publishDateSort	1998
publisher	Springer
record_format	marc
series	Lecture notes in physics
series2	Lecture notes in physics : New series : M, Monographs
spelling	Suzuki, Yasuyuki 1945- Verfasser (DE-588)120507862 aut Stochastic variational approach to quantum-mechanical few-body problems Yasuyuki Suzuki ; Kálmán Varga Berlin [u.a.] Springer 1998 XIV, 310 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics : New series : M, Monographs 54 Literaturverz. S. [299] - 305 Quantentheorie Few-body problem Quantum theory Random variables Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Wenigteilchensystem (DE-588)4129976-0 gnd rswk-swf Stochastische Optimierung (DE-588)4057625-5 gnd rswk-swf Variationsrechnung (DE-588)4062355-5 gnd rswk-swf Stochastik (DE-588)4121729-9 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Vielkörperproblem (DE-588)4078900-7 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf Variationsproblem (DE-588)4187419-5 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s DE-604 Schrödinger-Gleichung (DE-588)4053332-3 s Variationsrechnung (DE-588)4062355-5 s Vielkörperproblem (DE-588)4078900-7 s Stochastik (DE-588)4121729-9 s Eigenwert (DE-588)4151200-5 s Wenigteilchensystem (DE-588)4129976-0 s Quantenmechanisches System (DE-588)4300046-0 s Variationsproblem (DE-588)4187419-5 s Stochastische Optimierung (DE-588)4057625-5 s 1\p DE-604 Varga, Kálmán Verfasser aut Lecture notes in physics New series : M, Monographs ; 54 (DE-604)BV021852221 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015269689&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Suzuki, Yasuyuki 1945- Varga, Kálmán Stochastic variational approach to quantum-mechanical few-body problems Lecture notes in physics Quantentheorie Few-body problem Quantum theory Random variables Schrödinger-Gleichung (DE-588)4053332-3 gnd Wenigteilchensystem (DE-588)4129976-0 gnd Stochastische Optimierung (DE-588)4057625-5 gnd Variationsrechnung (DE-588)4062355-5 gnd Stochastik (DE-588)4121729-9 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Vielkörperproblem (DE-588)4078900-7 gnd Eigenwert (DE-588)4151200-5 gnd Variationsproblem (DE-588)4187419-5 gnd Quantenmechanik (DE-588)4047989-4 gnd
subject_GND	(DE-588)4053332-3 (DE-588)4129976-0 (DE-588)4057625-5 (DE-588)4062355-5 (DE-588)4121729-9 (DE-588)4300046-0 (DE-588)4078900-7 (DE-588)4151200-5 (DE-588)4187419-5 (DE-588)4047989-4
title	Stochastic variational approach to quantum-mechanical few-body problems
title_auth	Stochastic variational approach to quantum-mechanical few-body problems
title_exact_search	Stochastic variational approach to quantum-mechanical few-body problems
title_exact_search_txtP	Stochastic variational approach to quantum-mechanical few-body problems
title_full	Stochastic variational approach to quantum-mechanical few-body problems Yasuyuki Suzuki ; Kálmán Varga
title_fullStr	Stochastic variational approach to quantum-mechanical few-body problems Yasuyuki Suzuki ; Kálmán Varga
title_full_unstemmed	Stochastic variational approach to quantum-mechanical few-body problems Yasuyuki Suzuki ; Kálmán Varga
title_short	Stochastic variational approach to quantum-mechanical few-body problems
title_sort	stochastic variational approach to quantum mechanical few body problems
topic	Quantentheorie Few-body problem Quantum theory Random variables Schrödinger-Gleichung (DE-588)4053332-3 gnd Wenigteilchensystem (DE-588)4129976-0 gnd Stochastische Optimierung (DE-588)4057625-5 gnd Variationsrechnung (DE-588)4062355-5 gnd Stochastik (DE-588)4121729-9 gnd Quantenmechanisches System (DE-588)4300046-0 gnd Vielkörperproblem (DE-588)4078900-7 gnd Eigenwert (DE-588)4151200-5 gnd Variationsproblem (DE-588)4187419-5 gnd Quantenmechanik (DE-588)4047989-4 gnd
topic_facet	Quantentheorie Few-body problem Quantum theory Random variables Schrödinger-Gleichung Wenigteilchensystem Stochastische Optimierung Variationsrechnung Stochastik Quantenmechanisches System Vielkörperproblem Eigenwert Variationsproblem Quantenmechanik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015269689&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV021852221
work_keys_str_mv	AT suzukiyasuyuki stochasticvariationalapproachtoquantummechanicalfewbodyproblems AT vargakalman stochasticvariationalapproachtoquantummechanicalfewbodyproblems

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