Stochastic variational approach to quantum-mechanical few-body problems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1998
|
| Schriftenreihe: | Lecture notes in physics
New series : M, Monographs ; 54 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [299] - 305 |
| Beschreibung: | XIV, 310 S. graph. Darst. |
| ISBN: | 3540651527 |
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| 245 | 1 | 0 | |a Stochastic variational approach to quantum-mechanical few-body problems |c Yasuyuki Suzuki ; Kálmán Varga |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1998 | |
| 300 | |a XIV, 310 S. |b graph. Darst. | ||
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| 500 | |a Literaturverz. S. [299] - 305 | ||
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Datensatz im Suchindex
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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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| author | Suzuki, Yasuyuki 1945- Varga, Kálmán |
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| author_facet | Suzuki, Yasuyuki 1945- Varga, Kálmán |
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| bvnumber | BV022054961 |
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| callnumber-label | QC174 |
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| callnumber-sort | QC 3174.17 P7 |
| callnumber-subject | QC - Physics |
| classification_rvk | UD 8221 UL 1000 |
| ctrlnum | (OCoLC)40104946 (DE-599)BVBBV022054961 |
| dewey-full | 530.14 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14 |
| dewey-search | 530.14 |
| dewey-sort | 3530.14 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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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 |